// Numbas version: finer_feedback_settings
{"name": "word problem using graphical simultaneous equations 2.", "extensions": ["geogebra", "random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "word problem using graphical simultaneous equations 2.", "tags": [], "metadata": {"description": "<p>Students are shown to intersecting lines in the context of comparing the costs of services from two companies. They are asked to identify the y-intercept, the gradients, the point of intersection and are asked to interpret the graphs in the context of the word problem.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p></p>\n<p>You have a document that you want printed.</p>\n<p>{name1}'s company charges \\${b1} to&nbsp;set up&nbsp;the job, and \\${m1} for each&nbsp;copy&nbsp;of the document printed.</p>\n<p>{name2}'s company charges a \\${b2} to&nbsp;set up&nbsp;the job, and \\${m2} for each&nbsp;copy&nbsp;of the document printed.</p>\n<p>Your&nbsp;secretary prepared the following graph to illustrate this information, but {they1} did not give the axes meaningful names, and forgot to label the lines.</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/uky4vz3z',defs)}</p>", "advice": "<p>The two variables that are linearly related are number of documents and cost. Number of documents is the independent variable, so it should be on the horizontal axis, and cost should be on the vertical axis.</p>\n<p>The&nbsp;black line represents&nbsp;the costs of using {name1}'s company because this line has a $y$-intercept at {b1}, which matches the setup costs for {name1}'s company.</p>\n<p>If you intend to&nbsp;print {n} copies of the document, <span data-jme-visible=\"(m1*n+b1)&lt;(m2*n+b2)\">the cheaper option is&nbsp;to use {name1}'s company&nbsp;because this line has a lower value at the point where $x=\\var{n}$&nbsp;<span data-jme-visible=\"(m1*n+b1)&gt;(m2*n+b2)\">the cheaper option is&nbsp;to use {name2}'s company because this line has a lower value at the point where $x=\\var{n}$</span></span>&nbsp;<span data-jme-visible=\"(m1*n+b1)=(m2*n+b2)\">it doesn't matter which option you choose because the cost is the same</span>.</p>\n<p><span data-jme-visible=\"gymwins=1\">The&nbsp;least number of&nbsp;documents for which it is cheaper to&nbsp;use {name1}'s company&nbsp;is {px+gymwins}. This is the first $x$-axis value for which the {name1} company line is below the&nbsp;{name2} company line.</span></p>\n<p><span data-jme-visible=\"gymwins=-1\">The&nbsp;greatest number of&nbsp;documents for which it is cheaper to&nbsp;use {name2}'s company is {px+gymwins}. This the last $x$-axis value for which&nbsp;the {name2} company line is below the&nbsp;{name1} company line.</span></p>\n<p><span data-jme-visible=\"gymwins=0\">{px}&nbsp;visits are required for the costs to be equal for the two companies. This is the point at which the two lines intersect, and the cost is \\${m2*px+b2}.</span></p>\n<p><span data-jme-visible=\"whichperson=1\">The cost of printing&nbsp;{n2} document at {name1}'s company&nbsp;can be read from the graph using the&nbsp;{name1} company&nbsp;line. This is equal to \\${m1*n2+b1}.</span></p>\n<p><span data-jme-visible=\"whichperson=2\">The cost of&nbsp;printing&nbsp;{n2} documents at {name2}'s company can be read from the graph using the&nbsp;{name2} company&nbsp;line. This is equal to \\${m2*n2+b2}.</span></p>", "rulesets": {}, "extensions": ["geogebra", "random_person"], "variables": {"defs": {"name": "defs", "group": "lines", "definition": "[\n  ['b1',b1],['m1',m1],['b2',b2],['m2',m2],\n  ['xmin',0],['xmax',xmax],['ymin',0],['ymax',ymax]\n  ]", "description": "", "templateType": "anything"}, "m1": {"name": "m1", "group": "lines", "definition": "random(1..m2-1)", "description": "", "templateType": "anything"}, "m2": {"name": "m2", "group": "lines", "definition": "random(2..5)", "description": "", "templateType": "anything"}, "b2": {"name": "b2", "group": "lines", "definition": "random(1..10)", "description": "", "templateType": "anything"}, "xmax": {"name": "xmax", "group": "lines", "definition": "2*px", "description": "", "templateType": "anything"}, "px": {"name": "px", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "<p>the x-value of the intersection point</p>", "templateType": "anything"}, "ymax": {"name": "ymax", "group": "lines", "definition": "2*m1*px+b1", "description": "", "templateType": "anything"}, "gymwins": {"name": "gymwins", "group": "randomisers", "definition": "random(-1,0,1)", "description": "", "templateType": "anything"}, "person1": {"name": "person1", "group": "name variables", "definition": "people[0]", "description": "", "templateType": "anything"}, "neutral1": {"name": "neutral1", "group": "name variables", "definition": "person1['gender']='neutral'", "description": "", "templateType": "anything"}, "name1": {"name": "name1", "group": "name variables", "definition": "person1['name']", "description": "", "templateType": "anything"}, "they1": {"name": "they1", "group": "name variables", "definition": "person1['pronouns']['they']", "description": "", "templateType": "anything"}, "their1": {"name": "their1", "group": "name variables", "definition": "person1['pronouns']['their']", "description": "", "templateType": "anything"}, "theirs1": {"name": "theirs1", "group": "name variables", "definition": "person1['pronouns']['theirs']", "description": "", "templateType": "anything"}, "them1": {"name": "them1", "group": "name variables", "definition": "person1['pronouns']['them']", "description": "", "templateType": "anything"}, "themself1": {"name": "themself1", "group": "name variables", "definition": "person1['pronouns']['themself']", "description": "", "templateType": "anything"}, "s1": {"name": "s1", "group": "name variables", "definition": "if(neutral1,'','s')", "description": "", "templateType": "anything"}, "neutral2": {"name": "neutral2", "group": "name variables", "definition": "person1['gender']='neutral'", "description": "", "templateType": "anything"}, "name2": {"name": "name2", "group": "name variables", "definition": "person2['name']", "description": "", "templateType": "anything"}, "they2": {"name": "they2", "group": "name variables", "definition": "person2['pronouns']['they']", "description": "", "templateType": "anything"}, "their2": {"name": "their2", "group": "name variables", "definition": "person2['pronouns']['their']", "description": "", "templateType": "anything"}, "theirs2": {"name": "theirs2", "group": "name variables", "definition": "person2['pronouns']['theirs']", "description": "", "templateType": "anything"}, "them2": {"name": "them2", "group": "name variables", "definition": "person2['pronouns']['them']", "description": "", "templateType": "anything"}, "themself2": {"name": "themself2", "group": "name variables", "definition": "person2['pronouns']['themself']", "description": "", "templateType": "anything"}, "s2": {"name": "s2", "group": "name variables", "definition": "if(neutral1,'','s')", "description": "", "templateType": "anything"}, "whichperson": {"name": "whichperson", "group": "randomisers", "definition": "random(1,2)", "description": "", "templateType": "anything"}, "b1": {"name": "b1", "group": "lines", "definition": "m2*px+b2-m1*px", "description": "", "templateType": "anything"}, "person2": {"name": "person2", "group": "name variables", "definition": "people[1]", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(1..xmax)", "description": "<p>number of documents to print</p>", "templateType": "anything"}, "n2": {"name": "n2", "group": "Ungrouped variables", "definition": "random(2..xmax)", "description": "", "templateType": "anything"}, "people": {"name": "people", "group": "name variables", "definition": "random_people(30)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["px", "n", "n2"], "variable_groups": [{"name": "name variables", "variables": ["person1", "neutral1", "name1", "they1", "their1", "theirs1", "them1", "themself1", "s1", "neutral2", "name2", "they2", "their2", "theirs2", "them2", "themself2", "s2", "person2", "people"]}, {"name": "randomisers", "variables": ["whichperson", "gymwins"]}, {"name": "lines", "variables": ["m1", "m2", "b1", "b2", "xmax", "ymax", "defs"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "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>What is an appropriate label for the $x$-axis?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["number&nbsp;of documents", "cost ($)", "best number of documents to print", "Cheapest printing costs ($)"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "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>What is an appropriate label for the $y$-axis?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["number of documents", "Cost ($)", "best number of documents to print", "cheapest printing costs ($)"], "matrix": [0, "1", 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "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>Which line represents the cost of&nbsp;using&nbsp;{name1}'s company?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["red line", "black line"], "matrix": ["0", "1"], "distractors": ["", ""]}, {"type": "1_n_2", "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>If you intend to print {n} copies of the document, which is the cheaper option?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["{name1}'s company", "{name2}'s company", "it doesn't matter because they are the same price"], "matrix": ["if((m1*n+b1)<(m2*n+b2),1,0)", "if((m1*n+b1)>(m2*n+b2),1,0)", "if((m1*n)=(m2*n+b2),1,0)"], "distractors": ["", "", ""]}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><span data-jme-visible=\"gymwins=1\">What is the fewest number of&nbsp;documents for which it is cheaper to use {name2}'s company?</span></p>\n<p><span data-jme-visible=\"gymwins=-1\">What is the most number of&nbsp;documents for which it is cheaper to use {name1}'s company?</span></p>\n<p><span data-jme-visible=\"gymwins=0\">How many documents need to be printed for the costs to be the same for both companies?</span></p>", "minValue": "px+gymwins", "maxValue": "px+gymwins", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><span data-jme-visible=\"whichperson=1\">How many dollars&nbsp;does {name1}'s company charge to print&nbsp;{n2} documents?</span></p>\n<p><span data-jme-visible=\"whichperson=2\">How many dollars&nbsp;does {name2}'s company charge to print&nbsp;{n2} document?</span></p>", "minValue": "if(whichperson=1,m1*n2+b1,m2*n2+b2)", "maxValue": "if(whichperson=1,m1*n2+b1,m2*n2+b2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}