// Numbas version: exam_results_page_options
{"name": "Ann's copy of 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": [{"parts": [{"stepsPenalty": 1, "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        ", "marks": 0, "scripts": {}, "steps": [{"type": "information", "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": {}, "showCorrectAnswer": true}], "type": "gapfill", "gaps": [{"checkvariablenames": false, "showpreview": true, "scripts": {}, "expectedvariablenames": [], "type": "jme", "notallowed": {"partialCredit": 0, "showStrings": false, "message": "<p>Input as a fraction or an integer, not as a decimal.</p>", "strings": ["."]}, "answersimplification": "std", "vsetrangepoints": 5, "marks": 2, "checkingtype": "absdiff", "checkingaccuracy": 0.0001, "answer": "{an1}/{an2}", "vsetrange": [0, 1], "showCorrectAnswer": true}], "showCorrectAnswer": true}], "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "changing the subject of an equation", "checked2015", "rearranging equations", "SFY0001", "solving", "solving equations", "subject of an equation"], "variable_groups": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Solve for $x$: $\\displaystyle \\frac{s}{ax+b} = \\frac{t}{cx+d}$</p>", "notes": "\n        \t\t        \t\t\t\t\t\t        \t\t    \t\t\t\t        \n        \t\t"}, "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    ", "preamble": {"css": "", "js": ""}, "functions": {}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickQuestions": 0, "questions": [], "pickingStrategy": "all-ordered"}], "type": "question", "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>", "variables": {"t": {"definition": "random(2..8 except s)", "description": "", "group": "Ungrouped variables", "name": "t", "templateType": "anything"}, "s": {"definition": "random(2..8)", "description": "", "group": "Ungrouped variables", "name": "s", "templateType": "anything"}, "a": {"definition": "random(2..9 except [s,abs(b)])", "description": "", "group": "Ungrouped variables", "name": "a", "templateType": "anything"}, "d": {"definition": "random(-9..9 except [0,t])", "description": "", "group": "Ungrouped variables", "name": "d", "templateType": "anything"}, "c": {"definition": "random(2..9 except [s,abs(d),a*t/s])", "description": "", "group": "Ungrouped variables", "name": "c", "templateType": "anything"}, "an2": {"definition": "s*c-a*t", "description": "", "group": "Ungrouped variables", "name": "an2", "templateType": "anything"}, "an1": {"definition": "b*t-s*d", "description": "", "group": "Ungrouped variables", "name": "an1", "templateType": "anything"}, "b": {"definition": "random(-9..9 except [0,s])", "description": "", "group": "Ungrouped variables", "name": "b", "templateType": "anything"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "name": "Ann's copy of Solve an equation with reciprocals", "ungrouped_variables": ["a", "c", "b", "d", "s", "t", "an2", "an1"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Ann Smith", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2295/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Ann Smith", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2295/"}]}