// Numbas version: exam_results_page_options {"name": "W2a: Solve an equation with reciprocals-2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "parts": [{"showCorrectAnswer": true, "scripts": {}, "sortAnswers": false, "prompt": "\n

\$\\simplify{{s} / ({a} * x + {b}) = {t} / ({c} * x + {d})}\$

\n

$x=\\;$ [[0]]

\n

If you want help in solving the equation, click on Show steps. If you do so then you will lose 1 mark.

\n \n \n ", "type": "gapfill", "gaps": [{"showCorrectAnswer": true, "checkingAccuracy": 0.0001, "valuegenerators": [], "answerSimplification": "std", "variableReplacementStrategy": "originalfirst", "marks": 2, "useCustomName": false, "vsetRangePoints": 5, "variableReplacements": [], "unitTests": [], "scripts": {}, "type": "jme", "customName": "", "showFeedbackIcon": true, "showPreview": true, "adaptiveMarkingPenalty": 0, "failureRate": 1, "checkingType": "absdiff", "checkVariableNames": false, "notallowed": {"strings": ["."], "partialCredit": 0, "showStrings": false, "message": "

Input as a fraction or an integer, not as a decimal.

"}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "vsetRange": [0, 1], "answer": "{an1}/{an2}"}], "customName": "", "showFeedbackIcon": true, "adaptiveMarkingPenalty": 0, "stepsPenalty": 1, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "marks": 0, "steps": [{"showCorrectAnswer": true, "scripts": {}, "prompt": "\n

Rearrange the equation by cross-multiplying to get:
\$\\simplify{{s}*({c} * x + {d}) = {t} *({a} * x + {b})}\$
Multiply out to get \$\\simplify{{s*c}*x+{s*d}={t*a}*x+{t*b}}.\$ Now solve this linear equation.

\n \n ", "type": "information", "customName": "", "showFeedbackIcon": true, "adaptiveMarkingPenalty": 0, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "marks": 0, "useCustomName": false, "variableReplacements": [], "unitTests": []}], "useCustomName": false, "variableReplacements": [], "unitTests": []}], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "metadata": {"description": "

Solve for $x$: $\\displaystyle \\frac{s}{ax+b} = \\frac{t}{cx+d}$

", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "s", "t", "an2", "an1"], "name": "W2a: Solve an equation with reciprocals-2", "advice": "

Rearrange the equation by cross-multiplying to get:
\$\\simplify{{s}*({c} * x + {d}) = {t} *({a} * x + {b})}\$
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}}.\$

", "statement": "\n

Solve the following equation for $x$.

\n

Input your answer as a fraction or an integer as appropriate and not as a decimal.

\n ", "extensions": [], "variables": {"s": {"name": "s", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..8)"}, "c": {"name": "c", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..9 except [s,abs(d),a*t/s])"}, "b": {"name": "b", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-9..9 except [0,s])"}, "d": {"name": "d", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-9..9 except [0,t])"}, "a": {"name": "a", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..9 except [s,abs(b)])"}, "t": {"name": "t", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..8 except s)"}, "an1": {"name": "an1", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "b*t-s*d"}, "an2": {"name": "an2", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "s*c-a*t"}}, "variable_groups": [], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Timur Zaripov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3272/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Timur Zaripov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3272/"}]}