// Numbas version: finer_feedback_settings
{"name": "Luis'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": [{"ungrouped_variables": ["a", "c", "b", "d", "s", "t", "an2", "an1"], "metadata": {"description": "<p>Solve for $x$: $\\displaystyle \\frac{s}{ax+b} = \\frac{t}{cx+d}$</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variables": {"an1": {"description": "", "group": "Ungrouped variables", "definition": "b*t-s*d", "templateType": "anything", "name": "an1"}, "d": {"description": "", "group": "Ungrouped variables", "definition": "random(-9..9 except [0,t])", "templateType": "anything", "name": "d"}, "a": {"description": "", "group": "Ungrouped variables", "definition": "random(2..9 except [s,abs(b)])", "templateType": "anything", "name": "a"}, "b": {"description": "", "group": "Ungrouped variables", "definition": "random(-9..9 except [0,s])", "templateType": "anything", "name": "b"}, "s": {"description": "", "group": "Ungrouped variables", "definition": "random(2..8)", "templateType": "anything", "name": "s"}, "c": {"description": "", "group": "Ungrouped variables", "definition": "random(2..9 except [s,abs(d),a*t/s])", "templateType": "anything", "name": "c"}, "t": {"description": "", "group": "Ungrouped variables", "definition": "random(2..8 except s)", "templateType": "anything", "name": "t"}, "an2": {"description": "", "group": "Ungrouped variables", "definition": "s*c-a*t", "templateType": "anything", "name": "an2"}}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "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>", "parts": [{"scripts": {}, "sortAnswers": false, "extendBaseMarkingAlgorithm": true, "marks": 0, "gaps": [{"scripts": {}, "showPreview": true, "extendBaseMarkingAlgorithm": true, "marks": 2, "answer": "{an1}/{an2}", "checkingType": "absdiff", "notallowed": {"message": "<p>Input as a fraction or an integer, not as a decimal.</p>", "strings": ["."], "partialCredit": 0, "showStrings": false}, "type": "jme", "customMarkingAlgorithm": "", "answerSimplification": "std", "checkVariableNames": false, "showFeedbackIcon": true, "unitTests": [], "showCorrectAnswer": true, "expectedVariableNames": [], "vsetRangePoints": 5, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "failureRate": 1, "checkingAccuracy": 0.0001, "vsetRange": [0, 1]}], "type": "gapfill", "customMarkingAlgorithm": "", "showFeedbackIcon": true, "unitTests": [], "showCorrectAnswer": true, "stepsPenalty": 1, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "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        ", "steps": [{"showFeedbackIcon": true, "scripts": {}, "extendBaseMarkingAlgorithm": true, "type": "information", "unitTests": [], "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            ", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0, "customMarkingAlgorithm": ""}]}], "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "extensions": [], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "tags": [], "statement": "<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Resuelve la siguiente ecuaci&oacute;n para $ x $.</span></span></p>\n<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Ingrese su respuesta como una fracci&oacute;n o un entero, seg&uacute;n corresponda y no como un decimal.</span></span></p>", "name": "Luis's copy of Solve an equation with reciprocals", "type": "question", "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/"}]}