// Numbas version: exam_results_page_options
{"name": "Simultaneous equations", "metadata": {"description": "<p>Practise solving simultaneous linear equations graphically and algebraically.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "random-subset", "pickQuestions": "2", "questionNames": ["", "", "", ""], "questions": [{"name": "Identify profit and loss from a simultaneous equation graph", "extensions": [], "custom_part_types": [], "resources": [["question-resources/simultaneous_VNJzg0U.png", "/srv/numbas/media/question-resources/simultaneous_VNJzg0U.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Students are asked to find either the initial production cost, or a gradient, or the break even point from a graph.<br />They are then asked to determine the profit or loss from the graph for the production of a particular number of units. This number is randomised.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>The graph shows the cost of producing pencils and the revenue raised by selling them.</p>\n<p><img src=\"resources/question-resources/simultaneous_VNJzg0U.png\"/></p>", "advice": "<p>{advice}</p>\n<p>When {n} units are sold, from the graph, the revenue (income) is equal to {currency(1*n,'\\\\$','')}, and the costs are equal to {currency(0.5*n+20,'\\\\$','')}.</p>\n<p>profit&nbsp;= income - costs = {currency(1*n,'\\\\$','')} -&nbsp;{currency(0.5*n+20,'\\\\$','')} = {currency(profit,'\\\\$','')}.</p>\n<p>A positive number indicates a profit while a negative number indicates a loss.</p>\n<p>The gradient of the cost line is the cost to make one unit.</p>\n<p>The gradient of the income line&nbsp;is the income received from one unit. This is because gradient = rise over run, which is the incomefrom making $n$ units, divided by $n$, which equals the&nbsp;income&nbsp;from one unit.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"questionlist": {"name": "questionlist", "group": "Ungrouped variables", "definition": "[\n  'How many pencils need to be sold to break even?',\n  'What is the production setup cost, in dollars?',\n  'What is the gradient of the revenue line?',\n  'What is the gradient of the cost line?'\n  ]", "description": "", "templateType": "anything", "can_override": false}, "answerlist": {"name": "answerlist", "group": "Ungrouped variables", "definition": "[40,20,1,0.5]", "description": "", "templateType": "anything", "can_override": false}, "idx": {"name": "idx", "group": "Ungrouped variables", "definition": "random(0..3)", "description": "<p>choose between the 4 possible questions.</p>", "templateType": "anything", "can_override": false}, "question": {"name": "question", "group": "Ungrouped variables", "definition": "questionlist[idx]", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "answerlist[idx]", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(1..11)*5", "description": "", "templateType": "anything", "can_override": false}, "profit": {"name": "profit", "group": "Ungrouped variables", "definition": "1*n - (0.5*n+20)", "description": "", "templateType": "anything", "can_override": false}, "advicelist": {"name": "advicelist", "group": "Ungrouped variables", "definition": "[\n'The break even point occurs where the two lines meet. At this point, the number can be read from the horizontal axis, and is equal to 3 boxes.',\n  'The production setup cost is the cost when no boxes are manufactured. This is $20.',\n  'Gradient is rise / run. When the revenue line goes up by 10 units, it goes across by 10 unit, so the gradient is 10 divided by 10 = 1',\n  'Gradient is rise / run. When the revenue line goes up by 5 units, it goes across by 10 unit, so the gradient is 5 divided by 10 = 0.5'\n]", "description": "", "templateType": "anything", "can_override": false}, "advice": {"name": "advice", "group": "Ungrouped variables", "definition": "advicelist[idx]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["questionlist", "answerlist", "idx", "question", "answer", "n", "profit", "advicelist", "advice"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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>{question}</p>", "minValue": "answer", "maxValue": "answer", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "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>What is the profit or loss in dollars when {n}&nbsp;pencils are sold?</p>\n<p>Enter a profit as a positive number (for example, 20) but enter loss as a negative number (for example, -20)</p>", "minValue": "profit", "maxValue": "profit", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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>Write down an equation for the cost graph.&nbsp;</p>\n<p>$c$ represents cost, and $n$ represents the number of pencils made.</p>\n<p>$c = $ [[0]] $\\times n + $ [[1]]</p>", "gaps": [{"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, "minValue": "0.5", "maxValue": "0.5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "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, "minValue": "20", "maxValue": "20", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"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>Write down an equation for the income line.&nbsp;</p>\n<p>$r$ represents revenue (income), and $n$ represents the number of pencils made.</p>\n<p>$r = $ [[0]] $\\times n$</p>", "gaps": [{"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, "minValue": "1", "maxValue": "1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "information", "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 does the cost line gradient represent?&nbsp;</p>\n<p>What does the income line gradient represent?</p>\n<p>Write down your answers. You can check your answers after you have completed this question by choosing \"reveal solutions\".</p>"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Finding the break even point from a graph", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Students are shown a graph that simultaneously plots cost and revenue lines. They are asked to identify the break-even point.</p>\n<p>They are asked to give the x- and y- coordinate values.</p>\n<p>The graph is randomised, but it is set up so that the point of intersection lies on gridlines.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>The graph shows (in red) the cost of producing {items} and (in black) the revenue from selling them.</p>\n<p>The number of units is shown on the $x$-axis and the production cost in dollars is shown on the $y$-axis.</p>\n<p></p>\n<p>{geogebra_applet(\"https://www.geogebra.org/m/srpxwjnu\",defs)}</p>", "advice": "<p></p>\n<p>The break even point occurs where the two lines meet.</p>\n<p>This is at {x} on the horizontal axis, and {y} on the vertical axis.</p>\n<p>So {x} units need to be sold in order to break even, leading to a revenue of \\${y}, costs of \\${y} and a profit of \\$0.</p>", "rulesets": {}, "variables": {"shoptypes": {"name": "shoptypes", "group": "Ungrouped variables", "definition": "['bakery','bakery','bakery','craft shop','craft shop','craft shop']", "description": "", "templateType": "anything"}, "itemidx": {"name": "itemidx", "group": "Ungrouped variables", "definition": "random(0..5)", "description": "", "templateType": "anything"}, "itemtypes": {"name": "itemtypes", "group": "Ungrouped variables", "definition": "['tubs of ice cream','mobile phones','chairs','bouquets of flowers','heaters','boxes of apples']", "description": "", "templateType": "anything"}, "msellprices": {"name": "msellprices", "group": "Ungrouped variables", "definition": "[random(6,10),random(200,300,400),random(50,100,150),random(20,40,80,100),random(200,400,600),random(10,20,40)]", "description": "", "templateType": "anything"}, "mcost": {"name": "mcost", "group": "Ungrouped variables", "definition": "msell/2", "description": "", "templateType": "anything"}, "bcost": {"name": "bcost", "group": "Ungrouped variables", "definition": "bcostprices[itemidx]", "description": "", "templateType": "anything"}, "defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[\n  ['b1',0],['m1',msell],['b2',bcost],['m2',mcost],\n  ['xmin',-1],['xmax',2*x],['ymin',-1],['ymax',2*y]\n  ]", "description": "", "templateType": "anything"}, "shop": {"name": "shop", "group": "Ungrouped variables", "definition": "shoptypes[itemidx]", "description": "", "templateType": "anything"}, "item": {"name": "item", "group": "Ungrouped variables", "definition": "itemtypes[itemidx]", "description": "", "templateType": "anything"}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "bcost/(msell-mcost)", "description": "<p>break-even point x-value</p>", "templateType": "anything"}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "msell * x", "description": "<p>break even point y-value</p>", "templateType": "anything"}, "msell": {"name": "msell", "group": "Ungrouped variables", "definition": "msellprices[itemidx]", "description": "", "templateType": "anything"}, "bcostprices": {"name": "bcostprices", "group": "Ungrouped variables", "definition": "[15,600,150,200,600,20]", "description": "", "templateType": "anything"}, "unitschoices": {"name": "unitschoices", "group": "Ungrouped variables", "definition": "[]", "description": "", "templateType": "anything"}, "questionlist": {"name": "questionlist", "group": "Ungrouped variables", "definition": "['revenue is received','cost is incurred','profit is earned']", "description": "", "templateType": "anything"}, "questionidx": {"name": "questionidx", "group": "Ungrouped variables", "definition": "random(0,1,2)", "description": "", "templateType": "anything"}, "question": {"name": "question", "group": "Ungrouped variables", "definition": "questionlist[questionidx]", "description": "", "templateType": "anything"}, "answerlist": {"name": "answerlist", "group": "Ungrouped variables", "definition": "[y,y,0]", "description": "", "templateType": "anything"}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "answerlist[questionidx]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["shoptypes", "itemidx", "itemtypes", "msellprices", "mcost", "bcost", "defs", "shop", "item", "x", "y", "msell", "bcostprices", "unitschoices", "questionlist", "questionidx", "question", "answerlist", "answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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>How many units need to be sold in order to break even?</p>", "minValue": "x", "maxValue": "x", "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>How much&nbsp;{question} in dollars at the break-even point?</p>", "minValue": "answer", "maxValue": "answer", "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"}, {"name": "Graphical solution of simultaneous linear equations", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Studnents are asked to write down equations for cost and income for a business.</p>\n<p>They are then asked to graph the two lines.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>A&nbsp;{shop} owner sells&nbsp;{item}s for {currency(msell,\"\\\\$\",\"\")} each. It costs {currency(mcost,\"\\\\$\",\"\")} to make each {item} and {currency(bcost,\"\\\\$\",\"\")} for the equipment needed to make the {item}s.</p>", "advice": "<p>The income received from selling the {item}s is the selling cost of each item multiplied by the number of items sold.</p>\n<p>That is, $I = \\var{msell} \\times n$.</p>\n<p>The equation for income is a straight line of the form $y = mx +b$, where $m$ is the gradient of the line and $b$ is the $y$-intercept.</p>\n<p>In this equation, the&nbsp;constant $b = 0$ as, when 0 units are sold, $I=\\$0$, so the line passes through the point $(0,0)$.</p>\n<p>The cost to make the {item}s is the cost to make each item multiplied by the number of items made plus the fixed costs.</p>\n<p>That is, $C = \\var{mcost} \\times n + \\var{bcost}$.</p>\n<p>This is also a straight line of the form $y=mx+b$</p>\n<p>When we graph the two functions, we get the following:</p>\n<p>{geogebra_applet(\"https://www.geogebra.org/m/srpxwjnu\",defs)}</p>\n<p>Your graph needs:</p>\n<ul>\n<li>to start at (0,0) in the bottom left hand corner.</li>\n<li>to show the cost line and the revenue line.</li>\n<li>labels and arrows on both axes.</li>\n<li>a scale on each axis.</li>\n<li>to include the break-even point, where the two lines meet.</li>\n</ul>\n<p>You may have chosen different scales for your axes. This is fine.</p>\n<p></p>", "rulesets": {}, "variables": {"shoptypes": {"name": "shoptypes", "group": "Ungrouped variables", "definition": "['bakery','bakery','bakery','craft shop','craft shop','craft shop']", "description": "", "templateType": "anything"}, "itemidx": {"name": "itemidx", "group": "Ungrouped variables", "definition": "random(0..5)", "description": "", "templateType": "anything"}, "itemtypes": {"name": "itemtypes", "group": "Ungrouped variables", "definition": "['muffin','cake','pie','handmade paper','figurine','bandanna']", "description": "", "templateType": "anything"}, "msell": {"name": "msell", "group": "Ungrouped variables", "definition": "random(30..100)/10", "description": "", "templateType": "anything"}, "mcost": {"name": "mcost", "group": "Ungrouped variables", "definition": "round(random(10..msell*20/3))/10", "description": "", "templateType": "anything"}, "bcost": {"name": "bcost", "group": "Ungrouped variables", "definition": "random(1..10)*100", "description": "", "templateType": "anything"}, "defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[\n  ['b1',0],['m1',msell],['b2',bcost],['m2',mcost],\n  ['xmin',-1],['xmax',2*x],['ymin',-1],['ymax',2*y]\n  ]", "description": "", "templateType": "anything"}, "shop": {"name": "shop", "group": "Ungrouped variables", "definition": "shoptypes[itemidx]", "description": "", "templateType": "anything"}, "item": {"name": "item", "group": "Ungrouped variables", "definition": "itemtypes[itemidx]", "description": "", "templateType": "anything"}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "bcost/(msell-mcost)", "description": "<p>break-even point x-value</p>", "templateType": "anything"}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "msell * x", "description": "<p>break even point y-value</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["shoptypes", "itemidx", "itemtypes", "msell", "mcost", "bcost", "defs", "shop", "item", "x", "y"], "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>Write an equation to relate the income, $I$, that is made from selling the {item}s, to the $n$, the number of {item}s sold.</p>\n<p>Don't enter any dollar signs, just numbers.</p>\n<p>$I = $ [[0]]$\\times n +$[[1]]</p>", "gaps": [{"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, "minValue": "msell", "maxValue": "msell", "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, "minValue": "0", "maxValue": "0", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"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>Write an equation to relate the cost, $C$,&nbsp;of producing&nbsp;the {item}s, to the $n$, the number of {item}s sold.</p>\n<p>Don't enter any dollar signs, just numbers.</p>\n<p>$C = $&nbsp;[[0]]$\\times n +$[[1]]</p>", "gaps": [{"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, "minValue": "mcost", "maxValue": "mcost", "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, "minValue": "bcost", "maxValue": "bcost", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "information", "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>Draw up a table of values for each equation and plot the two lines on the same graph.</p>\n<p>You can check your graph yourself by clicking on the \"reveal answers\" button at the end of the question.</p>\n<p>Warning: Don't do this until you have finished the question, because it has answers for all of the question parts!</p>"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Solution of a word problem using graphical simultaneous equations.", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Students are shown to intersecting lines in the context of a gym visiting program. 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>A gym offers casual visits and memberships.</p>\n<p>For a casual visit, you pay a fixed amount each time you visit the gym.</p>\n<p>For a membership, you pay an upfront fee, and then a smaller amount each time you visit the gym.</p>\n<p>The graph&nbsp;the relationship between cost (in dollars) ($y$) and number of visits to the gym ($x$) for the two programs.</p>\n<p></p>\n<p>{geogebra_applet('https://www.geogebra.org/m/uky4vz3z',defs)}</p>", "advice": "<p>The red line represents the gym membership option because the line has a non-zero $y$-intercept which represents the value of the upfront payment.</p>\n<p></p>\n<p>If you intend to visit the gym {visits1}&nbsp;times, <span data-jme-visible=\"(m1*visits1)&lt;(m2*visits1+b2)\">the cheaper option is using casual visits&nbsp;because this line has a lower value at the point where $x=\\var{visits1}$</span>&nbsp;<span data-jme-visible=\"(m1*visits1)&gt;(m2*visits1+b2)\">the cheaper option is using a gym membership because this line has a lower value at the point where $x=\\var{visits1}$</span>&nbsp;<span data-jme-visible=\"(m1*visits1)=(m2*visits1+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 fewest number of visits for which it is cheaper to take out a gym membership is {k+gymwins}. This is the first $x$-axis value for which the gym membership line is below the casual visit line.</span></p>\n<p><span data-jme-visible=\"gymwins=-1\">The most number of visits for which it is cheaper to pay for casual visits is {k+gymwins}. This the last $x$-axis value for which the casual visit line is below the gym membership line.</span></p>\n<p><span data-jme-visible=\"gymwins=0\">{k}&nbsp;visits are required for the cost of a gym membership to equal the cost of the casual visits. This is the point at which the two lines intersect.</span></p>\n<p>The cost of the upfront payment for gym membership is the point at which the gym membership line cuts the $y$-axis, which is at \\${b2}.</p>\n<p><span data-jme-visible=\"visittype=0\">The cost of entry to the gym on a casual visit is the gradient of the casual visit line. It is also the value of the casual visit line when $x$=1 (1 visit). This is equal to {m1}.</span></p>\n<p><span data-jme-visible=\"visittype=1\">The cost of entry to the gym if you own a membership is the gradient of the gym membership line. This is given by vertical rise over horizontal run and is equal to {m2}.</span></p>\n<p>The graph is only meaningful at points where $x$ is a whole number because you cannot have fractional visits to the gym. For example, you cannot visit the gym 6.7 times.</p>", "rulesets": {}, "variables": {"defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[\n  ['b1',0],['m1',m1],['b2',b2],['m2',m2],\n  ['xmin',0],['xmax',xmax],['ymin',0],['ymax',ymax]\n  ]", "description": "", "templateType": "anything"}, "m1": {"name": "m1", "group": "Ungrouped variables", "definition": "random(15,20,25,30)", "description": "", "templateType": "anything"}, "m2": {"name": "m2", "group": "Ungrouped variables", "definition": "m1-b2/k", "description": "", "templateType": "anything"}, "b2": {"name": "b2", "group": "Ungrouped variables", "definition": "random(5..10)*10", "description": "", "templateType": "anything"}, "xmax": {"name": "xmax", "group": "Ungrouped variables", "definition": "1.5*k", "description": "", "templateType": "anything"}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(10)", "description": "<p>the x-value of the intersection point</p>", "templateType": "anything"}, "ymax": {"name": "ymax", "group": "Ungrouped variables", "definition": "1.5*m1*k", "description": "", "templateType": "anything"}, "visits1": {"name": "visits1", "group": "Ungrouped variables", "definition": "random(1..xmax)", "description": "", "templateType": "anything"}, "gymwins": {"name": "gymwins", "group": "Ungrouped variables", "definition": "random(-1,0,1)", "description": "", "templateType": "anything"}, "visittype": {"name": "visittype", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["defs", "m1", "m2", "b2", "xmax", "k", "ymax", "visits1", "gymwins", "visittype"], "variable_groups": [], "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>Which line represents the gym membership option?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["red line", "black line"], "matrix": ["1", 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>If you intend to visit the gym {visits1}&nbsp;times, which is the cheaper option?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["casual visits", "gym membership", "it doesn't matter because they are the same price"], "matrix": ["if((m1*visits1)<(m2*visits1+b2),1,0)", "if((m1*visits1)>(m2*visits1+b2),1,0)", "if((m1*visits1)=(m2*visits1+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 visits for which it is cheaper to take out a gym membership?</span></p>\n<p><span data-jme-visible=\"gymwins=-1\">What is the most number of visits for which it is cheaper to pay for casual visits?</span></p>\n<p><span data-jme-visible=\"gymwins=0\">How many visits are required for the cost of a gym membership to equal the cost of the casual visits?</span></p>", "minValue": "k+gymwins", "maxValue": "k+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>What is the&nbsp;cost of the upfront payment for gym membership?</p>", "minValue": "b2", "maxValue": "b2", "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=\"visittype=0\">What is the cost of entry to the gym on a casual visit?</span></p>\n<p><span data-jme-visible=\"visittype=1\">What is the cost of entry to the gym if you own a membership?</span></p>", "minValue": "if(visittype=0,m1,m2)", "maxValue": "if(visittype=0,m1,m2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "information", "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>Why is the graph only meaningful for the values where $x$ is a whole number?</p>"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "questions": [{"name": "Algebraic simultaneous equations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "tags": [], "metadata": {"description": "<p>Students are given 2 equations of the form y=mx+b and asked to solve them using either the substitution or the elimination method. The lines are randomised but the solution coordinates are always integers.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Use the {method} method to find the point of intersection of the following two lines.</p>\n<p>$y = \\var{m1}x \\var{b1sign} \\var{b1}$</p>\n<p>$y= \\var{m2}x \\var{b2sign} \\var{b2}$</p>", "advice": "<p><span data-jme-visible=\"method='substitution'\">To use the&nbsp;substitution method, we set the two expressions that are equal to $y$ equal to each other.</span></p>\n<p><span data-jme-visible=\"method='substitution'\">That is, </span></p>\n<p><span data-jme-visible=\"method='substitution'\">$\\var{m1}x \\var{b1sign}&nbsp;\\var{b1} = \\var{m2}x \\var{b2sign} \\var{b2}$</span></p>\n<p><span data-jme-visible=\"method='substitution'\">Then we subtract $\\var{m2}x$ from both sides:</span></p>\n<p><span data-jme-visible=\"method='substitution'\">$\\var{m1}x - \\var{m2}x \\var{b1sign} \\var{b1} =&nbsp; &nbsp;\\var{b2}$</span></p>\n<p><span data-jme-visible=\"method='substitution'\">In your working it is fine to replace '$--$' with '$+$' and '$+-$' with '$-$' if they ever appear.</span></p>\n<p><span data-jme-visible=\"method='substitution'\">The we&nbsp;subtract&nbsp;$\\var{b1}$ from both sides.&nbsp;</span></p>\n<p><span data-jme-visible=\"method='substitution'\">$\\var{m1}x -\\var{m2}x =&nbsp; \\var{b2} -&nbsp;\\var{b1} $</span></p>\n<p><span data-jme-visible=\"method='substitution'\">Now all the terms with $x$ are on one side, and all the terms without $x$ are on the other side.</span></p>\n<p><span data-jme-visible=\"method='substitution'\">Factorise out the $x$ on the left hand side:</span></p>\n<p><span data-jme-visible=\"method='substitution'\">$(\\var{m1} -\\var{m2})x =&nbsp; \\var{b2} -&nbsp;\\var{b1} $</span></p>\n<p><span data-jme-visible=\"method='substitution'\">Calculate $(\\var{m1} -\\var{m2})$ and $(\\var{b2}&nbsp;- \\var{b1})$</span></p>\n<p><span data-jme-visible=\"method='substitution'\">$(\\var{m1-m2})x =&nbsp; \\var{b2-b1} $</span></p>\n<p><span data-jme-visible=\"method='substitution'\">Finally, divide both sides by $\\var{m1-m2}$ to get</span></p>\n<p><span data-jme-visible=\"method='substitution'\">$x=\\var{(b2-b1)/(m1-m2)}$</span></p>\n<p><span data-jme-visible=\"method='elimination'\">To use the elimination method, let's start by giving the equations names so we can refer to them:</span></p>\n<p><span data-jme-visible=\"method='elimination'\">&nbsp;$ y = \\var{m1}x + \\var{b1} \\qquad \\qquad$ (1)</span></p>\n<p><span data-jme-visible=\"method='elimination'\">&nbsp;$ y =&nbsp;\\var{m2}x + \\var{b2} \\qquad \\qquad$ (2)</span></p>\n<p><span data-jme-visible=\"method='elimination'\">Let's calculate equation (1) - equation (2). This will eliminate the $y$ variable.</span></p>\n<p><span data-jme-visible=\"method='elimination'\">First just write out the subtraction. Make sure to put brackets around the two parts on the right hand side.</span></p>\n<p><span data-jme-visible=\"method='elimination'\">In your working it is fine to replace '$--$' with '$+$' and '$+-$' with '$-$' if they ever appear.</span></p>\n<p><span data-jme-visible=\"method='elimination'\">$ y - y = (\\var{m1}x + \\var{b1}) - (\\var{m2}x + \\var{b2})$</span></p>\n<p><span data-jme-visible=\"method='elimination'\">Then rearrange the right hand side:</span></p>\n<p><span data-jme-visible=\"method='elimination'\">$ 0 =&nbsp;\\var{m1}x + \\var{b1} - \\var{m2}x&nbsp;- \\var{b2}$</span></p>\n<p><span data-jme-visible=\"method='elimination'\">$ 0 =&nbsp;\\var{m1}x&nbsp;- \\var{m2}x + \\var{b1} -&nbsp;\\var{b2}$</span></p>\n<p><span data-jme-visible=\"method='elimination'\">Now calculate $\\var{b1} -&nbsp;\\var{b2}$</span></p>\n<p><span data-jme-visible=\"method='elimination'\">$ 0 =&nbsp;\\var{m1}x&nbsp;- \\var{m2}x + \\var{b1-b2}$</span></p>\n<p><span data-jme-visible=\"method='elimination'\">Add&nbsp;$\\var{b2-b1}$&nbsp;to both sides of the equation:</span></p>\n<p><span data-jme-visible=\"method='elimination'\">$\\var{b2-b1} =&nbsp;\\var{m1}x&nbsp;- \\var{m2}x$</span></p>\n<p><span data-jme-visible=\"method='elimination'\">Factorise the $x$ out on the right hand side.</span></p>\n<p><span data-jme-visible=\"method='elimination'\">$\\var{b2-b1} = (\\var{m1} - \\var{m2})x$</span></p>\n<p><span data-jme-visible=\"method='elimination'\">Calculate $&nbsp;&nbsp;(\\var{m1} - \\var{m2})$</span></p>\n<p><span data-jme-visible=\"method='elimination'\">$\\var{b2-b1} = (\\var{m1-m2})x$</span></p>\n<p><span data-jme-visible=\"method='elimination'\">Divide both sides by $(\\var{m1-m2})$</span></p>\n<p><span data-jme-visible=\"method='elimination'\">$\\var{(b2-b1)/(m1-m2)} = x$</span></p>\n<p><span data-jme-visible=\"method='elimination'\">So $x=\\var{px}$</span></p>\n<p>Now substitute this value for $x$ back into one of the original equations:</p>\n<p>$y = \\var{m1} \\times \\var{px} \\var{b1sign}&nbsp;\\var{b1}$</p>\n<p>$y = \\var{m1*px+b1}$</p>\n<p>The point of intersection is $(\\var{px},\\var{py})$.</p>\n<p>We can check that this point is correct by substituting it back into both of the original equations and seeing that they are both correct.</p>\n<p></p>", "rulesets": {}, "variables": {"m1": {"name": "m1", "group": "Unnamed group", "definition": "random(-1,1)*random(1..6)", "description": "", "templateType": "anything"}, "m2temp": {"name": "m2temp", "group": "Unnamed group", "definition": "random(-1,1)*random(1..6)", "description": "", "templateType": "anything"}, "m2": {"name": "m2", "group": "Unnamed group", "definition": "if(m1=m2temp,m2temp*(-1),m2temp)", "description": "", "templateType": "anything"}, "b1": {"name": "b1", "group": "Unnamed group", "definition": "random(-10..10)", "description": "", "templateType": "anything"}, "b2": {"name": "b2", "group": "Unnamed group", "definition": "(m1-m2)*px+b1", "description": "", "templateType": "anything"}, "px": {"name": "px", "group": "Unnamed group", "definition": "random(-10..10)", "description": "<p>Point of intersection, x-coordinate</p>", "templateType": "anything"}, "py": {"name": "py", "group": "Unnamed group", "definition": "m1*px+b1", "description": "<p>Point of intersection, y-coordinate</p>", "templateType": "anything"}, "method": {"name": "method", "group": "Ungrouped variables", "definition": "random('elimination','substitution')", "description": "", "templateType": "anything"}, "b1sign": {"name": "b1sign", "group": "display variables", "definition": "if(b1<0,\"\",\"$+$\")", "description": "", "templateType": "anything"}, "b2sign": {"name": "b2sign", "group": "display variables", "definition": "if(b2<0,\"\",\"$+$\")", "description": "", "templateType": "anything"}, "b1signneg": {"name": "b1signneg", "group": "display variables", "definition": "if(b1>0,\"\",\"$+$\")", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["method"], "variable_groups": [{"name": "Unnamed group", "variables": ["m1", "m2temp", "m2", "b1", "b2", "px", "py"]}, {"name": "display variables", "variables": ["b1sign", "b2sign", "b1signneg"]}], "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>The point of intersection occurs at</p>\n<p>$ x=$ [[0]]</p>\n<p>$y= $ [[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, 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false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "<p>This set of&nbsp;3 practice questions will change each time that you open them.</p>\n<p>After you have attempted a question, press \"submit answer\" and it will tell you whether or not you are correct.</p>\n<p>After you have attempted a question, you can see a worked solution. Press \"reveal answers\", then click \"OK\" on the popup message. A worked solution will appear at the bottom of the screen.</p>\n<p>If you would like more practice on a particular type of question,&nbsp;click \"Try another question like this one\", and click \"OK\" on the popup message. A new version of the same question will appear.</p>\n<p>If your screen is large enough, you can go to any question that you wish via the menu on the left hand side. Otherwise, you can scroll through the questions using the arrow buttons at the top left of the screen.</p>", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "extensions": ["geogebra"], "custom_part_types": [], "resources": [["question-resources/simultaneous_VNJzg0U.png", "/srv/numbas/media/question-resources/simultaneous_VNJzg0U.png"]]}