// Numbas version: exam_results_page_options
{"name": "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": [{"variable_groups": [], "variables": {"q": {"group": "Ungrouped variables", "templateType": "anything", "definition": "p*c/a", "description": "", "name": "q"}, "d": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-3..3 except 0)", "description": "", "name": "d"}, "a": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1..5 except [p,abs(b)])", "description": "", "name": "a"}, "c": {"group": "Ungrouped variables", "templateType": "anything", "definition": "m*a/g", "description": "", "name": "c"}, "t": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-3..3 except r)", "description": "", "name": "t"}, "r": {"group": "Ungrouped variables", "templateType": "anything", "definition": "(p*d+c*s-b*q)/a", "description": "", "name": "r"}, "an1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "b*t-s*d", "description": "", "name": "an1"}, "s": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-3..3 except 0)", "description": "", "name": "s"}, "an2": {"group": "Ungrouped variables", "templateType": "anything", "definition": "p*d+s*c-a*t-b*q", "description": "", "name": "an2"}, "b": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-3..3 except 0)", "description": "", "name": "b"}, "g": {"group": "Ungrouped variables", "templateType": "anything", "definition": "gcd(a,p)", "description": "", "name": "g"}, "p": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1..5)", "description": "", "name": "p"}, "m": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1..3)", "description": "", "name": "m"}}, "ungrouped_variables": ["a", "c", "b", "d", "g", "m", "q", "p", "s", "r", "t", "an2", "an1"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "name": "Solve an equation in algebraic fractions", "functions": {}, "showQuestionGroupNames": false, "parts": [{"marks": 0, "scripts": {}, "gaps": [{"answer": "{an1}/{an2}", "vsetrange": [0, 1], "checkingaccuracy": 0.0001, "checkvariablenames": false, "expectedvariablenames": [], "notallowed": {"showStrings": false, "message": "<p>Input as a fraction or an integer, not as a decimal.</p>", "strings": ["."], "partialCredit": 0}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "answersimplification": "std", "type": "jme", "showCorrectAnswer": true, "marks": 2, "vsetrangepoints": 5}], "type": "gapfill", "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": [{"type": "information", "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            ", "showCorrectAnswer": true, "marks": 0, "scripts": {}}], "showCorrectAnswer": true, "stepsPenalty": 1}], "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    ", "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "changing the subject of an equation", "checked2015", "rearranging equations", "SFY0001", "solving", "solving equations", "subject of an equation"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "\n        \t\t        \t\t\t\t\t        \t\t    \t\t\t\t        \n        \t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Solve for $x$: $\\displaystyle \\frac{px+s}{ax+b} = \\frac{qx+t}{cx+d}$ with $pc=qa$.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "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>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}