// Numbas version: exam_results_page_options
{"name": "Renaissance Algebra", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Renaissance Algebra", "tags": [], "metadata": {"description": "<p>Adaptiert von:&nbsp;Katz, V. J. (2009). <em>A history of mathematics: An introduction</em> (3. ed.). Boston: Addison-Wesley, S. 418.</p>", "licence": "Creative Commons Attribution-ShareAlike 4.0 International"}, "statement": "<p>Das folgende Problem&nbsp;stammt (bis auf die Zahlenwerte)&nbsp;&nbsp;von Piero della Francesca (1410/20-1492).</p>\n<p style=\"padding-left: 30px;\">Drei M&auml;nner gehen eine Gesch&auml;ftspartnerschaft ein. Der erste investiert {a} Dukaten in das Gesch&auml;ft, der zweite investiert {b} Dukaten und wir wissen nicht, wie viel der dritte investiert hat.</p>\n<p style=\"padding-left: 30px;\">Als Erl&ouml;s erhalten die drei&nbsp;Partner zusammen {sum} Dukaten, von denen der erste Partner {a2} Dukaten erh&auml;lt.</p>", "advice": "<p>Es ist davon auszugehen, dass der Erl&ouml;s aus dem Gesch&auml;ft proportional zur in die Partnerschaft investierten&nbsp;Summe ist.</p>\n<p>Der erste erh&auml;lt bei einer Investition von $\\var{a}$ Dukaten einen Erl&ouml;s von $\\var{a2}$ Dukaten.</p>\n<p>Dann muss der zweite bei einer Investition von {b} Dukaten einen Erl&ouml;s von $\\var{b}\\cdot\\frac{\\var{a2}}{\\var{a}}=\\var{b}\\cdot\\var{a2/a}=\\var{b2}$ Dukaten erhalten.</p>\n<p>F&uuml;r den dritten Partner bleiben dann vom Erl&ouml;s noch $\\var{sum}-\\var{a2}-\\var{b2}=\\var{c2}$ Dukaten &uuml;brig. Er hat demnach&nbsp;$\\var{c2}:\\frac{\\var{a2}}{\\var{a}}=\\var{c2}:\\var{a2/a}=\\var{c}$ Dukaten investiert gehabt.</p>\n<p>Im Original hat das Problem eine nicht-ganzzahlige L&ouml;sung, hier wurde als Erl&ouml;s zur Vereinfachung ein ganzzahliges Vielfaches der Investitionssume gew&auml;hlt.</p>", "rulesets": {}, "extensions": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "50+random(-1,1)*random(1..8)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "80+random(-1,1)*random(3,5,7)", "description": "", "templateType": "anything"}, "sum": {"name": "sum", "group": "Ungrouped variables", "definition": "(a+b+c0)*profit", "description": "", "templateType": "anything"}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "a*profit", "description": "", "templateType": "anything"}, "b2": {"name": "b2", "group": "Ungrouped variables", "definition": "b*a2/a", "description": "", "templateType": "anything"}, "c2": {"name": "c2", "group": "Ungrouped variables", "definition": "sum-a2-b2", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "c2*a/a2", "description": "", "templateType": "anything"}, "profit": {"name": "profit", "group": "Ungrouped variables", "definition": "random(3,5,6,7)", "description": "", "templateType": "anything"}, "c0": {"name": "c0", "group": "Ungrouped variables", "definition": "60+random(-1,1)*random(2,4,6,8)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "sum", "a2", "b2", "c2", "c", "profit", "c0"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Welche Anteile vom Erl&ouml;s erhalten der zweite und der dritte Partner und wie viel hatte der dritte investiert?</p>\n<p>Der zweite Mann erh&auml;lt&nbsp;[[0]] Dukaten vom Erl&ouml;s.</p>\n<p>Der dritte Mann erh&auml;lt&nbsp;[[1]] Dukaten vom Erl&ouml;s.</p>\n<p>Der dritte Mann hat&nbsp;[[2]] Dukaten investiert gehabt.</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "b2", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "b2", "maxValue": "b2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "c2", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "c2", "maxValue": "c2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain-eu"], "correctAnswerStyle": "plain-eu"}, {"type": "numberentry", "useCustomName": true, "customName": "c", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "c", "maxValue": "c", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain-eu"], "correctAnswerStyle": "plain-eu"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}]}]}], "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}]}