// Numbas version: exam_results_page_options
{"name": "Solve an equation with reciprocals", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"an1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "b*t-s*d", "description": "", "name": "an1"}, "d": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-9..9 except [0,t])", "description": "", "name": "d"}, "c": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9 except [s,abs(d),a*t/s])", "description": "", "name": "c"}, "s": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..8)", "description": "", "name": "s"}, "an2": {"group": "Ungrouped variables", "templateType": "anything", "definition": "s*c-a*t", "description": "", "name": "an2"}, "a": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9 except [s,abs(b)])", "description": "", "name": "a"}, "t": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..8 except s)", "description": "", "name": "t"}, "b": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-9..9 except [0,s])", "description": "", "name": "b"}}, "ungrouped_variables": ["a", "c", "b", "d", "s", "t", "an2", "an1"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Solve an equation with reciprocals", "functions": {}, "showQuestionGroupNames": false, "parts": [{"marks": 0, "scripts": {}, "gaps": [{"answer": "{an1}/{an2}", "showCorrectAnswer": true, "vsetrange": [0, 1], "checkingaccuracy": 0.0001, "checkvariablenames": false, "expectedvariablenames": [], "notallowed": {"message": "<p>Input as a fraction or an integer, not as a decimal.</p>", "showStrings": false, "partialCredit": 0, "strings": ["."]}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "answersimplification": "std", "marks": 2, "vsetrangepoints": 5}], "type": "gapfill", "showCorrectAnswer": true, "steps": [{"type": "information", "showCorrectAnswer": true, "prompt": "\n            <p>Rearrange the equation by cross-multiplying to get:<br/>\\[\\simplify{{s}*({c} * x + {d}) = {t} *({a} * x + {b})}\\]<br/>Multiply out to get \\[\\simplify{{s*c}*x+{s*d}={t*a}*x+{t*b}}.\\] Now solve this linear equation.</p>\n            \n            ", "marks": 0, "scripts": {}}], "prompt": "\n        <p>\\[\\simplify{{s} / ({a} * x + {b})  = {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        ", "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    ", "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "changing the subject of an equation", "checked2015", "rearranging equations", "SFY0001", "solving", "solving equations", "subject of an equation"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "\n        \t\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 $x$: $\\displaystyle \\frac{s}{ax+b} = \\frac{t}{cx+d}$</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>Rearrange the equation by cross-multiplying to get:<br/>\\[\\simplify{{s}*({c} * x + {d}) = {t} *({a} * x + {b})}\\]<br/>Multiply out to get \\[\\simplify{{s*c}*x+{s*d}={t*a}*x+{t*b}}.\\] Now this is a linear equation which is solved in the following steps: \\[\\simplify{{s*c-t*a}*x={t*b-s*d}}\\] and then \\[\\simplify{x={t*b-s*d}/{s*c-t*a}}.\\]</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/"}]}