// Numbas version: finer_feedback_settings
{"name": "Luis's copy of Solve an equation in algebraic fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": ["a", "c", "b", "d", "g", "m", "q", "p", "s", "r", "t", "an2", "an1"], "metadata": {"notes": "\n        \t\t        \t\t\t\t\t        \t\t    \t\t\t\t        \n        \t\t", "description": "<p>Solve for $x$: $\\displaystyle \\frac{px+s}{ax+b} = \\frac{qx+t}{cx+d}$ with $pc=qa$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "advice": "<p>Cross-multiply to get:<br/>\\[\\simplify{({p}*x+{s})*({c} * x + {d})=({q}*x+{t})*({a} * x + {b})}\\]<br/>Multiplying out we get \\[\\simplify{{p*c}x^2 +{p*d+c*s}x+{s*d}={q*a}x^2 +{q*b+t*a}x+{t*b}}\\] Subtracting ${\\var{a*q}}x^2$ from each side we are left with \\[\\simplify{{p*d+c*s}x+{s*d}={q*b+t*a}x+{t*b}}\\] which we solve as a linear equation: \\[\\simplify{{p*d+c*s-q*b-t*a}x={t*b-s*d}}\\] and so \\[\\simplify{x={an1}/{an2}}.\\]</p>", "showQuestionGroupNames": false, "variable_groups": [], "preamble": {"css": "", "js": ""}, "type": "question", "variablesTest": {"maxRuns": 100, "condition": ""}, "functions": {}, "parts": [{"scripts": {}, "showCorrectAnswer": true, "type": "gapfill", "stepsPenalty": 1, "gaps": [{"scripts": {}, "marks": 2, "showpreview": true, "answer": "{an1}/{an2}", "expectedvariablenames": [], "vsetrangepoints": 5, "type": "jme", "vsetrange": [0, 1], "checkvariablenames": false, "showCorrectAnswer": true, "checkingtype": "absdiff", "notallowed": {"message": "<p>Input as a fraction or an integer, not as a decimal.</p>", "partialCredit": 0, "strings": ["."], "showStrings": false}, "answersimplification": "std", "checkingaccuracy": 0.0001}], "marks": 0, "prompt": "\n        <p>\\[\\simplify{({p}*x+{s}) / ({a} * x + {b})  = ({q}*x+{t}) / ({c} * x + {d})}\\]</p>\n      <p>$x=\\;$ [[0]]</p>\n      <p>If you want help in solving the equation, click on Show steps. If you do so then you will lose 1 mark.</p>\n      \n        \n        ", "steps": [{"scripts": {}, "marks": 0, "prompt": "\n            <p>Cross-multiply to get:<br/>\\[\\simplify{({p}*x+{s})*({c} * x + {d})=({q}*x+{t})*({a} * x + {b})}\\]<br/>Multiplying out to get \\[\\simplify{{p*c}x^2 +{p*d+c*s}x+{s*d}={q*a}x^2 +{q*b+t*a}x+{t*b}}.\\] Subtract the $x^2$ term from each side to leave a linear equation: </p>\n          <p>Solve this equation for $x$.</p>\n            \n            ", "type": "information", "showCorrectAnswer": true}]}], "question_groups": [{"questions": [], "pickingStrategy": "all-ordered", "pickQuestions": 0, "name": ""}], "statement": "\n    <p>Solve the following equation for $x$.</p>\n  <p>Input your answer as a fraction or an integer as appropriate and not as a decimal.</p>\n    \n    ", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "changing the subject of an equation", "checked2015", "rearranging equations", "SFY0001", "solving", "solving equations", "subject of an equation"], "variables": {"r": {"description": "", "group": "Ungrouped variables", "definition": "(p*d+c*s-b*q)/a", "templateType": "anything", "name": "r"}, "b": {"description": "", "group": "Ungrouped variables", "definition": "random(-3..3 except 0)", "templateType": "anything", "name": "b"}, "a": {"description": "", "group": "Ungrouped variables", "definition": "random(1..5 except [p,abs(b)])", "templateType": "anything", "name": "a"}, "m": {"description": "", "group": "Ungrouped variables", "definition": "random(1..3)", "templateType": "anything", "name": "m"}, "s": {"description": "", "group": "Ungrouped variables", "definition": "random(-3..3 except 0)", "templateType": "anything", "name": "s"}, "c": {"description": "", "group": "Ungrouped variables", "definition": "m*a/g", "templateType": "anything", "name": "c"}, "q": {"description": "", "group": "Ungrouped variables", "definition": "p*c/a", "templateType": "anything", "name": "q"}, "an2": {"description": "", "group": "Ungrouped variables", "definition": "p*d+s*c-a*t-b*q", "templateType": "anything", "name": "an2"}, "an1": {"description": "", "group": "Ungrouped variables", "definition": "b*t-s*d", "templateType": "anything", "name": "an1"}, "g": {"description": "", "group": "Ungrouped variables", "definition": "gcd(a,p)", "templateType": "anything", "name": "g"}, "d": {"description": "", "group": "Ungrouped variables", "definition": "random(-3..3 except 0)", "templateType": "anything", "name": "d"}, "p": {"description": "", "group": "Ungrouped variables", "definition": "random(1..5)", "templateType": "anything", "name": "p"}, "t": {"description": "", "group": "Ungrouped variables", "definition": "random(-3..3 except r)", "templateType": "anything", "name": "t"}}, "name": "Luis's copy of Solve an equation in algebraic fractions", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}