![](\"http://2.bp.blogspot.com/-cth6k3e3jwQ/VQXfSRgqJHI/AAAAAAAABMI/wxS9Is8HCU8/s1600/bodmas.png\")
Linear equations, simultaneous linear equations in two variables
\nrebel
\nrebelmaths
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Remove the brackets and gather the x terms together and also the number terms together.
\nWhen in fraction form, get the lowest common multiple (LCM), and multiply the top line by how many times the divisor goes into the LCM.
\nRule for multiping out brackets:
\n(a$x$ - b)(c$x$ + d) = (a * c)$x^2$ + ((a * d) + ((-b) *c)))$x$ + ((-b) * d)
\nRule for squaring brackets:
\n(-a$x$ + b)$^2$ = (-a * -a)$x^2$ + (2 * (-a) *b)$x$ + (b * b)
", "rulesets": {"std": ["all", "!collectNumbers "]}, "parts": [{"prompt": "$\\var{num1p[0]}(\\var{num1p[1]}x + \\var{num1p[2]}) \\var{num1n[0]}(\\var{num1p[3]} \\var{num1n[1]}x) + \\var{num1p[4]}$
\n[[0]]
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\n[[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{ans43}x^2+{ans42}x+{ans41}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "$(\\var{n5[0]}x + \\var{p5[0]})^2$
\n[[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Don't forget to fully square out the bracket. $(ax + b)^2 = (ax + b)(ax + b)$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{ans53}x^2 +{ans52}x +{ans51}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "Express $\\frac{\\var{nm[0]}x}{\\var{dm[0]}} + \\frac{\\var{nm[1]}x}{\\var{dm[1]}}$ as a single fraction.
\n[[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "First you need to find a common denominator. To do this you need to find the lowest common multiple of the three denominator.
\nWatch video for help
\n", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "({ans2}x)/{ans1}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "$\\frac{\\var{p2[0]}x+ \\var{p2[1]}}{\\var{div[0]}}+\\frac{\\var{p2[2]} \\var{n2[0]}x}{\\var{div[1]}}-\\frac{\\var{p2[3]}x+ \\var{p2[4]}}{\\var{div[2]}}$
\n[[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "({ans21}+{ans22}x)/({dv1})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "$\\frac{\\var{t3[0]}}{\\var{d3[0]}}(\\var{p3[0]}x \\var{n3[0]})-\\frac{\\var{t3[1]}}{\\var{d3[1]}}(\\var{p3[1]} \\var{n3[1]}x)-\\frac{\\var{t3[2]}}{\\var{d3[2]}}(\\var{p3[2]}x + \\var{p3[3]})$
\n[[0]]
\n", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "({ans31}+{ans32}x)/({dv2})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "For the following, leave the numbers as is, do not put into lowest form as these are algebra expressions:
\nFor example:
\nWhen you simplify the equation and the answer is $3x -6$, leave it as that, do not answer $x - 2$.
", "variable_groups": [{"variables": ["dm", "nm", "ans1", "ans2"], "name": "new"}, {"variables": ["dv1", "dv2"], "name": "edt"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans1": {"definition": "lcm(dm[0],dm[1])", "templateType": "anything", "group": "new", "name": "ans1", "description": ""}, "ans2": {"definition": "((ans1/dm[0])nm[0]) + ((ans1/dm[1])nm[1])", "templateType": "anything", "group": "new", "name": "ans2", "description": ""}, "d3": {"definition": "shuffle([7,11,13])[0..3]", "templateType": "anything", "group": "Ungrouped variables", "name": "d3", "description": ""}, "ans53": {"definition": "n5[0]*n5[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans53", "description": ""}, "ans22": {"definition": "(p2[0]*div[1]*div[2])+(n2[0]*div[0]*div[2])-(p2[3]*div[1]*div[0])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "ans21": {"definition": "(p2[1]*div[1]*div[2])+(p2[2]*div[0]*div[2])-(p2[4]*div[1]*div[0])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}, "nm": {"definition": "shuffle([2,4,6,8,10])[0..2]", "templateType": "anything", "group": "new", "name": "nm", "description": ""}, "num1n": {"definition": "shuffle(-9..-2)[0..2]", "templateType": "anything", "group": "Ungrouped variables", "name": "num1n", "description": ""}, "ans41": {"definition": "n4[0]*p4[2]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans41", "description": ""}, "ans43": {"definition": "p4[0]*p4[1]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans43", "description": ""}, "ans42": {"definition": "(p4[0]*p4[2])+(p4[1]*n4[0])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans42", "description": ""}, "num1p": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "num1p", "description": ""}, "dv1": {"definition": "div[0]*div[1]*div[2]", "templateType": "anything", "group": "edt", "name": "dv1", "description": ""}, "dv2": {"definition": "d3[0]*d3[1]*d3[2]", "templateType": "anything", "group": "edt", "name": "dv2", "description": ""}, "dm": {"definition": "shuffle([3,5,7,11])[0..2]", "templateType": "anything", "group": "new", "name": "dm", "description": ""}, "ans12": {"definition": "(num1p[0]*num1p[1])+(num1n[0]*num1n[1])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12", "description": ""}, "ans11": {"definition": "(num1p[0]*num1p[2])+(num1n[0]*num1p[3])+ num1p[4]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "ans31": {"definition": "(n3[0]*d3[1]*d3[2]*t3[0])-(p3[1]*d3[0]*d3[2]*t3[1])-(p3[3]*d3[1]*d3[0]*t3[2])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans32": {"definition": "(p3[0]*d3[1]*d3[2]*t3[0])-(n3[1]*d3[0]*d3[2]*t3[1])-(p3[2]*d3[1]*d3[0]*t3[2])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "n2": {"definition": "shuffle(-9..-2)[0..8]", "templateType": "anything", "group": "Ungrouped variables", "name": "n2", "description": ""}, "p2": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "p2", "description": ""}, "p3": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "p3", "description": ""}, "p4": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "p4", "description": ""}, "p5": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "p5", "description": ""}, "ans52": {"definition": "n5[0]*p5[0]*2", "templateType": "anything", "group": "Ungrouped variables", "name": "ans52", "description": ""}, "t3": {"definition": "shuffle([2,3,4,5])[0..3]", "templateType": "anything", "group": "Ungrouped variables", "name": "t3", "description": ""}, "ans51": {"definition": "p5[0]*p5[0]", "templateType": "anything", "group": "Ungrouped variables", "name": "ans51", "description": ""}, "div": {"definition": "shuffle([3,5,7,9,11])[0..5]", "templateType": "anything", "group": "Ungrouped variables", "name": "div", "description": ""}, "n3": {"definition": "shuffle(-9..-2)[0..8]", "templateType": "anything", "group": "Ungrouped variables", "name": "n3", "description": ""}, "n4": {"definition": "shuffle(-9..-2)[0..8]", "templateType": "anything", "group": "Ungrouped variables", "name": "n4", "description": ""}, "n5": {"definition": "shuffle(-9..-2)[0..8]", "templateType": "anything", "group": "Ungrouped variables", "name": "n5", "description": ""}}, "metadata": {"description": "Simplifying algebraic expressions
\nrebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q2 (Algebra equations solve for x)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["num1p", "num1n", "ans11", "ans21", "numh", "num3p", "num3n", "posa", "nega", "ans41", "ans31", "posb", "neg", "ans51"], "tags": ["rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "Part 1:
\n$x$:
\n$\\frac{(\\var{numh[0]}-\\var{num1p[1]})}{(\\var{num1p[0]}-\\var{num1p[2]})} = \\var{ans11}$
\nPart 2:
\n$x$:
\n$\\frac{((\\var{num1p[7]} \\times \\var{num1p[6]})-(\\var{num1p[4]} \\times \\var{num1n[2]})}{((\\var{num1p[1]} \\times \\var{num1p[5]})-(\\var{num1p[7]} \\times \\var{num1n[7]})} = \\var{ans21}$
\nPart 3:
\n$x$:
\n$\\frac{((\\var{num3p[4]} \\times \\var{num3p[5]})+\\var{num3p[6]}+(\\var{num3n[4]} \\times \\var{num3n[5]})-\\var{num3p[0]}-(\\var{num3p[1]} \\times \\var{num3n[0]})-(\\var{num3n[1]} \\times \\var{num3n[2]}))} {((\\var{num3p[1]} \\times \\var{num3p[2]})+(\\var{num3n[1]} \\times \\var{num3p[3]})-(\\var{num3p[4]} \\times \\var{num3n[3]})-(\\var{num3n[4]} \\times \\var{num3p[7]}))} = \\var{ans31}$
\nPart 4:
\n$x$:
\n$\\frac{(\\var{nega[3]}-\\frac{\\var{nega[1]}}{\\var{posa[1]}}+\\frac{\\var{posa[5]}}{\\var{posa[3]}}-\\frac{\\var{nega[2]}}{\\var{posa[6]}})} {(\\frac{\\var{posa[2]}}{\\var{posa[1]}}-\\frac{\\var{posa[4]}}{\\var{posa[3]}}+\\frac{\\var{posa[7]}}{\\var{posa[6]}})} = \\var{ans41}$
\nPart 5:
\n$x$:
\n$\\frac{((\\var{posb[3]} \\times \\var{nega[4]}) - (\\var{posb[1]} \\times \\var{posb[5]}))}{((\\var{posb[1]} \\times \\var{posb[4]}) - (\\var{posb[3]} \\times \\var{posb[2]}))} = \\var{ans51}$
", "rulesets": {"std": ["all", "basic", "simplifyFractions"], "ruleset1": []}, "parts": [{"prompt": "$\\var{num1p[0]}x + \\var{num1p[1]} = \\var{num1p[2]}x + \\var{numh[0]}$
\n$x =$ [[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "({ans11}+0.5)", "strictPrecision": false, "minValue": "({ans11}-0.5)", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "$\\var{num1p[4]}(\\var{num1p[5]} \\var{num1n[2]}x) = \\var{num1p[7]}(\\var{num1p[6]} \\var{num1n[7]}x)$
\n$x =$ [[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "({ans21}+0.5)", "strictPrecision": false, "minValue": "({ans21}-0.5)", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": "0", "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "$\\var{num3p[0]} + \\var{num3p[1]}(\\var{num3p[2]}x \\var{num3n[0]})\\var{num3n[1]}(\\var{num3p[3]}x \\var{num3n[2]}) = \\var{num3p[4]}(\\var{num3p[5]} \\var{num3n[3]}x) + \\var{num3p[6]} \\var{num3n[4]}(\\var{num3p[7]}x \\var{num3n[5]})$
\n$x =$ [[0]]
\n", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}+0.5", "strictPrecision": false, "minValue": "{ans31}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "$\\frac{1}{\\var{posa[1]}}(\\var{posa[2]}x \\var{nega[1]})-\\frac{1}{\\var{posa[3]}}(\\var{posa[4]}x +\\var{posa[5]})+\\frac{1}{\\var{posa[6]}}(\\var{posa[7]}x \\var{nega[2]}) = \\var{nega[3]}$
\n$x =$ [[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Get a common denominator like in question 1. The multiply both sides of the equation by that common denominator to get rid of the fractions.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans41}+0.5", "strictPrecision": false, "minValue": "{ans41}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "$\\frac{\\var{posb[1]}}{\\var{posb[2]}x\\var{neg[4]}}= \\frac{\\var{posb[3]}}{\\var{posb[4]}x+\\var{posb[5]}}$
\n$x =$ [[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans51}+0.5", "strictPrecision": false, "minValue": "{ans51}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "Solve for $x$ in the following, to 2 decimal places:
\nWatch the video below for help with the questions:
\n", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"num3n": {"definition": "shuffle(-10..-2)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "num3n", "description": ""}, "num1n": {"definition": "shuffle(-9..-2)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "num1n", "description": ""}, "ans41": {"definition": "(nega[3]-(nega[1]/posa[1])+(posa[5]/posa[3])-(nega[2]/posa[6]))/((posa[2]/posa[1])-(posa[4]/posa[3])+(posa[7]/posa[6]))\n", "templateType": "anything", "group": "Ungrouped variables", "name": "ans41", "description": ""}, "posb": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "posb", "description": ""}, "posa": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "posa", "description": ""}, "ans11": {"definition": "(numh[0]-num1p[1])/(num1p[0]-num1p[2])", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "num1p": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "num1p", "description": ""}, "neg": {"definition": "shuffle(-9..-2)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "neg", "description": ""}, "ans31": {"definition": "((num3p[4] * num3p[5])+num3p[6]+(num3n[4] *num3n[5])-num3p[0]-(num3p[1] * num3n[0])-(num3n[1] * num3n[2])) / ((num3p[1] * num3p[2])+(num3n[1] * num3p[3])-(num3p[4] * num3n[3])-(num3n[4] * num3p[7])) ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "nega": {"definition": "shuffle(-9..-2)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "nega", "description": ""}, "num3p": {"definition": "shuffle(2..10)[0..9]", "templateType": "anything", "group": "Ungrouped variables", "name": "num3p", "description": ""}, "numh": {"definition": "shuffle(20..40)[0..15]", "templateType": "anything", "group": "Ungrouped variables", "name": "numh", "description": ""}, "ans21": {"definition": "((num1p[7] * num1p[6])-(num1p[4] * num1p[5]))/((num1p[4] * num1n[2])-(num1p[7] * num1n[7])) ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}, "ans51": {"definition": "((posb[3] * neg[4]) - (posb[1] * posb[5]))/((posb[1] * posb[4]) - (posb[3] * posb[2]))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans51", "description": ""}}, "metadata": {"description": "Simple Linear Equations involving basic transposition
\nrebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q3 (simultaneous equations, solve for x and y)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "a1", "b1", "c1", "ans1", "ans2", "a21", "a22", "a31", "a32", "b21", "b22", "b31", "b32", "ans21", "c21", "c22", "ans22", "ans31", "ans32", "c31", "c32"], "tags": ["rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "Have a look at this youtube video to understand simultaneous equations better: Simultaneous Equations
\nTo find x:
\n$\\frac{((\\var{b} \\times \\var{c1}) - (\\var{b1} \\times \\var{c}))}{((\\var{a1} \\times \\var{b}) - (\\var{a} \\times \\var{b1}))} = \\var{ans1}$
\nTo find y:
\n$\\frac{(\\var{c1} - (\\var{a1} \\times \\var{ans1}))}{\\var{b1}} = \\var{ans2}$
\n\nParts B and C are done using the same method.
\n", "rulesets": {"std": ["all"]}, "parts": [{"stepsPenalty": 0, "prompt": "$\\simplify{{a}x + {b}y = {c}}$
\n$\\simplify{{a1}x + {b1}y = {c1}}$
\nx: [[0]]
\ny: [[1]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "It might be helpful to multiply each equation by 10 first to get rid of the decimals.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}+0.5", "strictPrecision": false, "minValue": "{ans1}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans2} +0.5", "strictPrecision": false, "minValue": "{ans2} -0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "$\\simplify{{a21}x + {b21}y = {c21}}$
\n$\\simplify{{a22}x + {b22}y = {c22}}$
\nx: [[0]]
\ny: [[1]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans21}+0.5", "strictPrecision": false, "minValue": "{ans21}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans22} +0.5", "strictPrecision": false, "minValue": "{ans22} -0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "$\\simplify{{a31}x + {b31}y = {c31}}$
\n$\\simplify{{a32}x + {b32}y = {c32}}$
\nx: [[0]]
\ny: [[1]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}+0.5", "strictPrecision": false, "minValue": "{ans31}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans32} +0.5", "strictPrecision": false, "minValue": "{ans32} -0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "Solve for x and y:
\nCorrect to one decimal place!!
\nAlso make sure you do not round off too early!!!
", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a21": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a21", "description": ""}, "a22": {"definition": "random(1..9#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a22", "description": ""}, "ans1": {"definition": "(b*c1 - b1*c)/(a1*b - a*b1) ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "(c1 - a1*ans1)/(b1) ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "b22": {"definition": "random(-9..9#0.1 except[a21,0])", "templateType": "anything", "group": "Ungrouped variables", "name": "b22", "description": ""}, "b21": {"definition": "random(-9..9 except [0,a21])", "templateType": "anything", "group": "Ungrouped variables", "name": "b21", "description": ""}, "b1": {"definition": "random(-9..9 except[a1,0])", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "c1": {"definition": "random(-9..9 except [0,b1,round(b1/2),round(b1/3),round(b1/4),b1*2,b1*3,b1*4,b1*1.5,b1*2.5,b1*3.5,b1*4.5,round(b1/1.5),round(b1/2.5),round(b1/3.5),round(b1/4.5)])", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "ans21": {"definition": "(b21*c22 - b22*c21)/(a22*b21 - a21*b22) ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}, "ans22": {"definition": "(c22 - a22*ans21)/(b22) ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "c31": {"definition": "random(-9..9#0.1 except [0,b31,round(b31/2),round(b31/3),round(b31/4),b31*2,b31*3,b31*4,b31*1.5,b31*2.5,b31*3.5,b31*4.5,round(b31/1.5),round(b31/2.5),round(b31/3.5),round(b31/4.5)])", "templateType": "anything", "group": "Ungrouped variables", "name": "c31", "description": ""}, "c32": {"definition": "random(-9..9#0.1 except [0,b32,round(b32/2),round(b32/3),round(b32/4),b32*2,b32*3,b32*4,b32*1.5,b32*2.5,b32*3.5,b32*4.5,round(b32/1.5),round(b32/2.5),round(b32/3.5),round(b32/4.5)])", "templateType": "anything", "group": "Ungrouped variables", "name": "c32", "description": ""}, "a32": {"definition": "random(1..9#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a32", "description": ""}, "a31": {"definition": "random(1..9#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a31", "description": ""}, "b31": {"definition": "random(-9..9#0.1 except [0,a31])", "templateType": "anything", "group": "Ungrouped variables", "name": "b31", "description": ""}, "b32": {"definition": "random(-9..9#0.1 except[b21,0])", "templateType": "anything", "group": "Ungrouped variables", "name": "b32", "description": ""}, "a1": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "b": {"definition": "random(-9..9 except [0,a])", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "ans31": {"definition": "(b31*c32 - b32*c31)/(a32*b31 - a31*b32) ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans32": {"definition": "(c32 - a32*ans31)/(b32) ", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "a": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(-9..9 except [0,b,round(b/2),round(b/3),round(b/4),b*2,b*3,b*4,b*1.5,b*2.5,b*3.5,b*4.5,round(b/1.5),round(b/2.5),round(b/3.5),round(b/4.5)])", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "c21": {"definition": "random(-9..9 except [0,b21,round(b21/2),round(b21/3),round(b21/4),b21*2,b21*3,b21*4,b21*1.5,b21*2.5,b21*3.5,b21*4.5,round(b21/1.5),round(b21/2.5),round(b21/3.5),round(b21/4.5)])", "templateType": "anything", "group": "Ungrouped variables", "name": "c21", "description": ""}, "c22": {"definition": "random(-9..9#0.1 except [0,b22,round(b22/2),round(b22/3),round(b22/4),b22*2,b22*3,b22*4,b22*1.5,b22*2.5,b22*3.5,b22*4.5,round(b22/1.5),round(b22/2.5),round(b22/3.5),round(b22/4.5)])", "templateType": "anything", "group": "Ungrouped variables", "name": "c22", "description": ""}}, "metadata": {"description": "Simultaneous Linear Equations
\nrebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q4 (Calculating area using algebraic equations)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["lent1", "red1", "area1", "ans11", "ans12", "per2", "ratio2", "ans21", "ans22", "ans23", "lent3", "per3", "ans31", "ans32", "ratio4", "per4", "ans41", "ans42", "ans43"], "tags": ["area using algebra", "Rebel", "REBEL", "rebel", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "Have a look at this youtube video to understand simultaneous equations better: Simultaneous Equations
\nPart 1:
\nWidth:
\n$\\var{lent1} \\times (width - \\var{red1}) = \\var{area1}cm$
\n$ width: \\frac{(\\var{area1}+(\\var{red1} \\times \\var{lent1}))}{\\var{lent1}} = \\var{ans11}$
\nArea:
\n$\\var{lent1} \\times \\var{ans11}= \\var{ans12}cm^2$
\nPart 2:
\nWidth:
\n$(2 \\times Length)+ (2 \\times width) = \\var{per2}cm$
\n$Length = \\var{ratio2} \\times width$
\n$ width: \\frac{\\frac{\\var{per2}}{2}}{1 + \\var{ratio2}} = \\var{ans21}cm$
\nLength:
\n$\\var{ratio2} \\times \\var{ans21} = \\var{ans22}cm$
\nArea:
\n$\\var{ans21} \\times \\var{ans22}= \\var{ans23}cm^2$
\nPart 3:
\nSimilar to part 2
\nLength:
\n$\\frac{\\frac{\\var{per3}}{2}}{2 + \\frac{\\var{lent3}}{100}} = \\var{ans31}cm$
\nBreath:
\n$\\var{ans31} \\times (1 + \\frac{\\var{lent3}}{100}) = \\var{ans32}cm$
\nPart 4:
\nSimilar to part 2
\nWidth:
\n$\\frac{\\frac{\\var{per4}}{2}}{1 + \\var{ratio4}} = \\var{ans41}cm$
\nLength:
\n$\\var{ratio4} \\times \\var{ans41} = \\var{ans42}cm$
\nArea:
\n$\\var{ans41} \\times \\var{ans42}= \\var{ans43}cm^2$
\n", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "A rectangle has a length of $\\var{lent1} cm$ and a width of $x cm$. If the width was reduced by $\\var{red1} cm$, the area would be $\\var{area1} cm^2$. Find the original width and area of this rectangle.
\nWidth: [[0]]$cm$
\nArea: [[1]]$cm^2$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "First sketch the original rectangle with the information given. Next draw the second rectangle with the new width. How can you represent this new width using x? Now use the information given to find x.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans11}+0.5", "strictPrecision": false, "minValue": "{ans11}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans12}+0.5", "strictPrecision": false, "minValue": "{ans12}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "Find the width, length and area of a rectangler room which has a perimeter of $\\var{per2} m$, if its length is $\\var{ratio2}$ times its width.
\nWidth: [[0]]$m$
\nLength: [[1]]$m$
\nArea: [[2]]$m^2$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Sketch the rectangle and represent the information given in the question.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "({ans21}+0.5)", "strictPrecision": false, "minValue": "({ans21}-0.5)", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": "0", "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "({ans22}+0.5)", "strictPrecision": false, "minValue": "({ans22}-0.5)", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "({ans23}+0.5)", "strictPrecision": false, "minValue": "({ans23}-0.5)", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "The length of a rectangle is $\\var{lent3}$% greater than its breadth. If the perimeter of the rectangle is $\\var{per3} m$, find the length and breadth.
\nLength: [[0]]$m$
\nBreadth: [[1]]$m$
\n", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Convert the precentage to decimals. E.g. 30% bigger would mean the length was 1.3x.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}+0.5", "strictPrecision": false, "minValue": "{ans31}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans32}+0.5", "strictPrecision": false, "minValue": "{ans32}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "Find the width, length and area of a rectangle room which has a perimeter of $\\var{per4} m$, if its length is $\\var{ratio4}$ times its width.
\nWidth: [[0]]$m$
\nLength: [[1]]$m$
\nArea: [[2]]$m^2$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans41}+0.5", "strictPrecision": false, "minValue": "{ans41}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans42}+0.5", "strictPrecision": false, "minValue": "{ans42}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans43}+0.5", "strictPrecision": false, "minValue": "{ans43}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "Solve the following correct to 1 decimal place:
", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans12": {"definition": "ans11*lent1", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12", "description": ""}, "red1": {"definition": "random(2..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "red1", "description": ""}, "per2": {"definition": "random(32..80#4)", "templateType": "anything", "group": "Ungrouped variables", "name": "per2", "description": ""}, "ratio2": {"definition": "random(1.5..4.5#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "ratio2", "description": ""}, "ans41": {"definition": "(per4/2)/(1+ratio4)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans41", "description": ""}, "lent1": {"definition": "random(15..35)", "templateType": "anything", "group": "Ungrouped variables", "name": "lent1", "description": ""}, "ans43": {"definition": "ans41*ans42", "templateType": "anything", "group": "Ungrouped variables", "name": "ans43", "description": ""}, "lent3": {"definition": "random(15..35#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "lent3", "description": ""}, "per3": {"definition": "random(1.2..3.6#0.2)", "templateType": "anything", "group": "Ungrouped variables", "name": "per3", "description": ""}, "ratio4": {"definition": "random(1.25..4.75#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "ratio4", "description": ""}, "ans11": {"definition": "(area1+(red1*lent1))/lent1", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "area1": {"definition": "random(402..495#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "area1", "description": ""}, "per4": {"definition": "random(12.2..24.8#0.2 except[13..24])", "templateType": "anything", "group": "Ungrouped variables", "name": "per4", "description": ""}, "ans31": {"definition": "(per3/2)/(2+(lent3/100))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans32": {"definition": "ans31*(1+(lent3/100))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "ans42": {"definition": "ratio4*ans41", "templateType": "anything", "group": "Ungrouped variables", "name": "ans42", "description": ""}, "ans23": {"definition": "ans21*ans22", "templateType": "anything", "group": "Ungrouped variables", "name": "ans23", "description": ""}, "ans22": {"definition": "ratio2*ans21", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "ans21": {"definition": "(per2/2)/(1+ratio2)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}}, "metadata": {"description": "Algebra word problems using area and perimeter.
\nrebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q5 (Calculating wages using algebraic equations)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["num11", "num12", "wages1", "num13", "ans11", "ans12", "ans21", "ans22", "num21", "num22", "num23", "wages2", "num31", "num32", "wages3", "num33", "ans31", "ans32", "num41", "num42", "wages41", "num43", "wages42", "ans41", "ans42"], "tags": ["Rebel", "REBEL", "rebel", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "Have a look at this youtube video to understand simultaneous equations better: Simultaneous Equations
\nPart 1:
\nTradesman:
\nFind the Labourer's wage first, then:
\n$\\var{ans12} + \\var{num13} = €\\var{ans11}$
\nLabourer:
\n$\\frac{\\var{wages1} - (\\var{num11} \\times \\var{num13})}{(\\var{num11} + \\var{num12})} = €\\var{ans12}$
\nPart 2:
\nFirst identify the 2 simultaneous equations;
\nL + T = $\\var{num21}$
\n$\\var{num22}$L + $\\var{num23}T$ = $\\var{wages2}$
\nNo. of Labourers:
\nFind the no. of Tradesmen first, then:
\n$\\var{num21} - \\var{ans22} = \\var{ans21}$
\nNo. of Tradesmen:
\n$\\frac{((\\var{wages2} \\times 1) - (\\var{num22} \\times \\var{num21}))}{((\\var{num23} \\times 1) - (\\var{num22} \\times 1))} = \\var{ans22}$
\nPart 3:
\nTradesman:
\nFind the Labourer's wage first, then:
\n$\\var{ans32} + \\var{num33} = €\\var{ans31}$
\nLabourer:
\n$\\frac{\\var{wages3} - (\\var{num31} \\times \\var{num33})}{(\\var{num31} + \\var{num32})} = €\\var{ans32}$
\nPart 4:
\nTradesman:
\nFind the Labourer's wage first, then:
\n$\\var{wages42} - (\\var{num43} \\times \\var{num41}) = €\\var{ans41}$
\nLabourer:
\n$\\frac{\\var{wages41} - (\\var{num41} \\times \\var{wages42})}{(\\var{num42} - (\\var{num41} \\times \\var{num43}))} = €\\var{ans42}$
", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "$\\var{num41}$ tradesmen and $\\var{num42}$ labourers earn $€\\var{wages41}$ per week while 1 tradesman and $\\var{num43}$ labourers earn $€\\var{wages42}$ per week. Find the earnings for 1 tradesman and 1 labourer.
\nTradesmen: €[[0]]
\nLabourer: €[[1]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Create two simultaneous equations to describe the information given in the question.
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans42}+0.5", "strictPrecision": false, "minValue": "{ans42}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans41}+0.5", "strictPrecision": false, "minValue": "{ans41}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "$\\var{num11}$ tradesmen and $\\var{num12}$ labourers earn $€\\var{wages1}$ between them to do a job. If a tradesman earns $€\\var{num13}$ more than a labourer, calculate the earnings for a tradesman and a labourer.
\nTradesmen: €[[0]]
\nLabourer: €[[1]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans11}+0.5", "strictPrecision": false, "minValue": "{ans11}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans12}+0.5", "strictPrecision": false, "minValue": "{ans12}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "$\\var{num21}$ workmen on a building site earn a total of $€\\var{wages2}$ between them per week. Labourers are paid $€\\var{num22}$ per week and Tradesmen are paid $€\\var{num23}$ per week. How many of each is employed?
\n[[0]] Labourers
\n[[1]] Tradesmen
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans21}", "minValue": "{ans21}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans22}", "minValue": "{ans22}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "$\\var{num31}$ tradesmen and $\\var{num32}$ labourers earn $€\\var{wages3}$ between them to do a job. If a tradesman earns $€\\var{num33}$ more than a labour, calculate the earnings for a tradesman and a labourer.
\nTradesmen: €[[0]]
\nLabourer: €[[1]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}+0.5", "strictPrecision": false, "minValue": "{ans31}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans32}+0.5", "strictPrecision": false, "minValue": "{ans32}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "Calculate the following, to the nearest cent!!
", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"wages41": {"definition": "random(9000..11000)", "templateType": "anything", "group": "Ungrouped variables", "name": "wages41", "description": ""}, "wages42": {"definition": "random(2405..2795#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "wages42", "description": ""}, "ans22": {"definition": "random(3..12 except ans21)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "ans21": {"definition": "random(5..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}, "wages3": {"definition": "random(7005..8995#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "wages3", "description": ""}, "wages2": {"definition": "(ans21*num22)+(ans22*num23)", "templateType": "anything", "group": "Ungrouped variables", "name": "wages2", "description": ""}, "wages1": {"definition": "random(8000..9000)", "templateType": "anything", "group": "Ungrouped variables", "name": "wages1", "description": ""}, "ans41": {"definition": "(wages41-(wages42*num41))/(num42 -(num41*num43))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans41", "description": ""}, "ans42": {"definition": "wages42-(num43*ans41)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans42", "description": ""}, "num23": {"definition": "random(num22+140..800#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "num23", "description": ""}, "num22": {"definition": "random(500..600#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "num22", "description": ""}, "num21": {"definition": "ans21+ans22", "templateType": "anything", "group": "Ungrouped variables", "name": "num21", "description": ""}, "num41": {"definition": "random(5..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "num41", "description": ""}, "num43": {"definition": "random(3..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "num43", "description": ""}, "num42": {"definition": "random(7..9 except num41)", "templateType": "anything", "group": "Ungrouped variables", "name": "num42", "description": ""}, "ans12": {"definition": "(wages1-(num11*num13))/(num11+num12)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12", "description": ""}, "ans11": {"definition": "ans12+num13", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "ans31": {"definition": "ans32+num33", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans32": {"definition": "(wages3-(num31*num33))/(num31+num32)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "num12": {"definition": "random(4..7 except num11)", "templateType": "anything", "group": "Ungrouped variables", "name": "num12", "description": ""}, "num13": {"definition": "random(71..89 except[80])", "templateType": "anything", "group": "Ungrouped variables", "name": "num13", "description": ""}, "num11": {"definition": "random(7..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "num11", "description": ""}, "num31": {"definition": "random(4..11 except [num11,num21])", "templateType": "anything", "group": "Ungrouped variables", "name": "num31", "description": ""}, "num32": {"definition": "random(4..11 except [num11,num21,num31])", "templateType": "anything", "group": "Ungrouped variables", "name": "num32", "description": ""}, "num33": {"definition": "random(66..84 except[70,75,80])", "templateType": "anything", "group": "Ungrouped variables", "name": "num33", "description": ""}}, "metadata": {"description": "Calculating wages using algebraic equations
\nrebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q6 (Calculating cars/carparts using equations) ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["num11", "num12", "num13", "num14", "num15", "num16", "cost11", "ans11", "ans12", "cost12", "ans13", "num21", "num22", "num23", "num24", "num25", "num26", "cost21", "cost22", "ans21", "ans22", "ans23", "num31", "num32", "num33", "num34", "cost31", "cost32", "ans31", "ans32"], "tags": ["rebelmaths", "simultaneous equations", "Simultaneous equations", "teame", "word problem"], "preamble": {"css": "", "js": ""}, "advice": "Have a look at this youtube video to understand simultaneous equations better: Simultaneous Equations
\nPart 1:
\nTo find cost of Brand A:
\n$\\frac{((\\var{num12} \\times \\var{cost12}) - (\\var{num14} \\times \\var{cost11}))}{((\\var{num13} \\times \\var{num12}) - (\\var{num11} \\times \\var{num14}))} = €\\var{ans11}$
\nTo find cost of Brand B:
\n$\\frac{(\\var{cost12} - (\\var{num13} \\times \\var{ans11}))}{\\var{num14}} = €\\var{ans12}$
\nTo find total cost of $\\var{num15}$ Brand A tyres and $\\var{num16}$ Brand B tyres:
\n$(\\var{num15} \\times \\var{ans11}) + (\\var{num16} \\times \\var{ans12}) = €\\var{ans13}$
\nPart 2:
\nTo find cost of a new Car:
\n$\\frac{((\\var{num22} \\times \\var{cost22}) - (\\var{num24} \\times \\var{cost21}))}{((\\var{num23} \\times \\var{num22}) - (\\var{num21} \\times \\var{num24}))} = €\\var{ans21}$
\nTo find cost of a new Van:
\n$\\frac{(\\var{cost22} - (\\var{num23} \\times \\var{ans21}))}{\\var{num24}} = €\\var{ans22}$
\nTo find total cost of $\\var{num25}$ new Cars and $\\var{num26}$ new Vans:
\n$(\\var{num25} \\times \\var{ans21}) + (\\var{num26} \\times \\var{ans22}) = €\\var{ans23}$
\nPart 3:
\nTo find cost of a Model A Car:
\n$\\frac{((\\var{num32} \\times \\var{cost32}) - (\\var{num34} \\times \\var{cost31}))}{((\\var{num33} \\times \\var{num32}) - (\\var{num31} \\times \\var{num34}))} = €\\var{ans31}$
\nTo find cost of a Model B Car:
\n$\\frac{(\\var{cost32} - (\\var{num33} \\times \\var{ans31}))}{\\var{num34}} = €\\var{ans32}$
\n\n", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "$\\var{num31}$ cars of model A and $\\var{num32}$ cars of model B cost $€\\var{cost31}$, while $\\var{num33}$ cars of model A and $\\var{num34}$ cars of model B cost $€\\var{cost32}$. What is the cost of each model?
\nRound to the nearest euro.
\nModel A: €[[0]]
\nModel B: €[[1]]
\n", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Watch this video for help with the question:
\n", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}", "minValue": "{ans31}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans32}", "minValue": "{ans32}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "$\\var{num11}$ tyres of Brand A and $\\var{num12}$ tyres of Brand B cost €{dpformat(cost11,2)}. $\\var{num13}$ tyres of Brand A and $\\var{num14}$ tyres of Brand B cost €{dpformat(cost12,2)}. How much do $\\var{num15}$ tyres of Brand A and $\\var{num16}$ tyres of Brand B cost?
\nRound to the nearest cent.
\nBrand A: €[[0]]
\nBrand B: €[[1]]
\nTotal: €[[2]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans11}+0.5", "strictPrecision": false, "minValue": "{ans11}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans12}+0.5", "strictPrecision": false, "minValue": "{ans12}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans13}+1", "strictPrecision": false, "minValue": "{ans13}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "$\\var{num21}$ new Cars and $\\var{num22}$ new Vans cost $€\\var{cost21}$, while $\\var{num23}$ new Cars and $\\var{num24}$ new Vans cost $€\\var{cost22}$. Find the cost of $\\var{num25}$ new Cars and $\\var{num26}$ new Vans.
\nRound to the nearest euro.
\nNew Car: €[[0]]
\nNew Van: €[[1]]
\nTotal: €[[2]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans21}", "minValue": "{ans21}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans22}", "minValue": "{ans22}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans23}", "minValue": "{ans23}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "Solve the following:
", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"cost31": {"definition": "(num31*ans31)+(num32*ans32)", "templateType": "anything", "group": "Ungrouped variables", "name": "cost31", "description": ""}, "cost32": {"definition": "(num33*ans31)+(num34*ans32)", "templateType": "anything", "group": "Ungrouped variables", "name": "cost32", "description": ""}, "ans23": {"definition": "(num25*ans21)+(num26*ans22)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans23", "description": ""}, "ans22": {"definition": "random(11500..ans21-2000#100)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "ans21": {"definition": "random(14000..17000#100)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}, "cost12": {"definition": "(num13*ans11)+(num14*ans12)", "templateType": "anything", "group": "Ungrouped variables", "name": "cost12", "description": ""}, "cost11": {"definition": "(num11*ans11)+(num12*ans12)", "templateType": "anything", "group": "Ungrouped variables", "name": "cost11", "description": ""}, "num23": {"definition": "random(3..12 except [num21,num22])", "templateType": "anything", "group": "Ungrouped variables", "name": "num23", "description": ""}, "num22": {"definition": "random(3..12 except num21)", "templateType": "anything", "group": "Ungrouped variables", "name": "num22", "description": ""}, "num21": {"definition": "random(3..7 except num11)", "templateType": "anything", "group": "Ungrouped variables", "name": "num21", "description": ""}, "num26": {"definition": "random(3..12 except [num21,num22,num23,num24,num25])", "templateType": "anything", "group": "Ungrouped variables", "name": "num26", "description": ""}, "num25": {"definition": "random(3..12 except [num21,num22,num23,num24])", "templateType": "anything", "group": "Ungrouped variables", "name": "num25", "description": ""}, "num24": {"definition": "random(3..12 except [num21,num22,num23])", "templateType": "anything", "group": "Ungrouped variables", "name": "num24", "description": ""}, "ans12": {"definition": "random(75.5..99#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12", "description": ""}, "ans13": {"definition": "(num15*ans11)+(num16*ans12)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans13", "description": ""}, "cost21": {"definition": "(num21*ans21)+(num22*ans22)", "templateType": "anything", "group": "Ungrouped variables", "name": "cost21", "description": ""}, "ans11": {"definition": "random(55.5..70#5)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "ans31": {"definition": "random(17000..19000#200)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans32": {"definition": "random(22000..26000#500)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "cost22": {"definition": "(num23*ans21)+(num24*ans22)", "templateType": "anything", "group": "Ungrouped variables", "name": "cost22", "description": ""}, "num16": {"definition": "random(3..14 except [num11,num12,num13,num14,num15])", "templateType": "anything", "group": "Ungrouped variables", "name": "num16", "description": ""}, "num14": {"definition": "random(3..14 except [num11,num12,num13])", "templateType": "anything", "group": "Ungrouped variables", "name": "num14", "description": ""}, "num15": {"definition": "random(3..14 except [num11,num12,num13,num14])", "templateType": "anything", "group": "Ungrouped variables", "name": "num15", "description": ""}, "num12": {"definition": "random(3..14 except num11)", "templateType": "anything", "group": "Ungrouped variables", "name": "num12", "description": ""}, "num13": {"definition": "random(3..14 except [num11,num12])", "templateType": "anything", "group": "Ungrouped variables", "name": "num13", "description": ""}, "num11": {"definition": "random(3..14)", "templateType": "anything", "group": "Ungrouped variables", "name": "num11", "description": ""}, "num34": {"definition": "random(3..7 except [num31,num32,num33])", "templateType": "anything", "group": "Ungrouped variables", "name": "num34", "description": ""}, "num31": {"definition": "random(3..7 except [num11,num21])", "templateType": "anything", "group": "Ungrouped variables", "name": "num31", "description": ""}, "num32": {"definition": "random(3..7 except [num31])", "templateType": "anything", "group": "Ungrouped variables", "name": "num32", "description": ""}, "num33": {"definition": "random(3..7 except [num31,num32])", "templateType": "anything", "group": "Ungrouped variables", "name": "num33", "description": ""}}, "metadata": {"description": "Word Problems leading to simultaneous Linear Equations
\nrebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Q7 (simultaneous equations to solve forces in a system, and solve for x)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}], "functions": {}, "ungrouped_variables": ["a", "b", "c", "a1", "b1", "c1", "ans1", "ans2", "num1", "num2", "num3", "ans"], "tags": ["rebelmaths", "simultaneous equations", "Simultaneous equations", "teame"], "preamble": {"css": "", "js": ""}, "advice": "Have a look at this youtube video to understand simultaneous equations better: Simultaneous Equations
\nPart 1:
\nTo find $F_1$:
\n$\\frac{((\\var{b} \\times \\var{c1}) - (\\var{b1} \\times \\var{c}))}{((\\var{a1} \\times \\var{b}) - (\\var{a} \\times \\var{b1}))} = \\var{ans1}$
\nTo find $F_2$:
\n$\\frac{(\\var{c1} - (\\var{a1} \\times \\var{ans1}))}{\\var{b1}} = \\var{ans2}$
\nPart 2:
\n$\\frac{(-\\var{num3} - (\\var{num1}*\\var{num3}))}{((\\var{num1}*\\var{num2})-\\var{num2})} = \\var{ans}$
\n", "rulesets": {"std": ["all"]}, "parts": [{"prompt": "$\\simplify{{a}F_1 + {b}F_2 = {c}}$
\n$\\simplify{{a1}F_1 + {b1}F_2 = {c1}}$
\n$F_1$: [[0]]
\n$F_2$: [[1]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}+0.5", "strictPrecision": false, "minValue": "{ans1}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans2} +0.5", "strictPrecision": false, "minValue": "{ans2} -0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "Solve for $x$, correct to 2 decimal places:
\n$\\frac{\\var{num1}(\\var{num2}x + \\var{num3})}{\\var{num2}x - \\var{num3}} = 1$
\n$x=$ [[0]]
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans}+0.5", "strictPrecision": false, "minValue": "{ans}-0.5", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "The forces $F_1$ and $F_2$ in a system are described by the simultaneous equations given below.
\nSolve for $F_1$ and $F_2$:
\nCorrect to one decimal place!!
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\nrebelmaths
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