// Numbas version: exam_results_page_options
{"name": "David's copy of Using compound units - room hire price per hour and per minute", "extensions": ["random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"scripts": {}, "prompt": "<p>{name} is quoted a price of {pounds(block_price_per_hour*hours)} by ACME Office Services to book a room in advance for {hours} hours, or {pounds(single_price_per_hour)} per hour in a pay-as-you-go scheme.</p>\n<p>To compare the two prices, {pronouns['they']} decide{verbs} to convert the advance booking price to a price per hour.</p>\n<p>Price per hour: &pound; [[0]]</p>", "showFeedbackIcon": true, "gaps": [{"showPrecisionHint": true, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "showFeedbackIcon": true, "minValue": "block_price_per_hour", "precisionType": "dp", "type": "numberentry", "strictPrecision": false, "maxValue": "block_price_per_hour", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "precision": "2", "mustBeReducedPC": 0, "scripts": {}, "mustBeReduced": false, "precisionPartialCredit": 0, "showCorrectAnswer": true, "correctAnswerFraction": false, "marks": "1", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"]}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}, {"scripts": {}, "prompt": "<p>A competitor, RoomCo, is offering meeting rooms charged by the minute, at {pounds(competitor_price_per_minute)} per minute.</p>\n<p>To compare this price to ACME's offer, {name} decide{verbs} to convert it to a price per hour.</p>\n<p>Price per hour: &pound;&nbsp;[[0]]</p>\n<p></p>", "showFeedbackIcon": true, "gaps": [{"showPrecisionHint": true, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "showFeedbackIcon": true, "minValue": "60*competitor_price_per_minute", "precisionType": "dp", "type": "numberentry", "strictPrecision": false, "maxValue": "60*competitor_price_per_minute", "allowFractions": false, "variableReplacementStrategy": "originalfirst", "precision": "2", "mustBeReducedPC": 0, "scripts": {}, "mustBeReduced": false, "precisionPartialCredit": 0, "showCorrectAnswer": true, "correctAnswerFraction": false, "marks": 1, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"]}], "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}, {"maxMarks": 0, "showFeedbackIcon": true, "type": "1_n_2", "variableReplacementStrategy": "originalfirst", "displayColumns": "1", "scripts": {}, "prompt": "<p>How should {name} book the room?</p>", "displayType": "radiogroup", "matrix": "marking_matrix", "minMarks": 0, "choices": ["<p>Pay in advance at ACME</p>", "<p>Pay-as-you-go at ACME</p>", "<p>Pay per minute at RoomCo</p>"], "showCorrectAnswer": true, "marks": 0, "variableReplacements": [], "shuffleChoices": false}], "tags": ["taxonomy"], "advice": "<h4>a)</h4>\n<p>The price per hour is the total price divide by the number of hours.</p>\n<p>\\[ \\text{Price per hour} = \\frac{\\var{block_price_per_hour*hours}}{\\var{hours}} = &pound;\\var{dpformat(block_price_per_hour,2)} \\text{ per hour} \\]</p>\n<h4>b)</h4>\n<p>The price is given in pence per minute. To convert to pounds per&nbsp;minute, divide by $100$:</p>\n<p>\\[ \\var{100*competitor_price_per_minute} \\text{ p/minute} = &pound;\\var{dpformat(competitor_price_per_minute,2)} \\text{ per minute} \\]</p>\n<p>Then to convert to pounds per hour, multiply by $60$:</p>\n<p>\\[ &pound;\\var{dpformat(competitor_price_per_minute,2)} \\text{ per minute} = &pound;\\var{dpformat(competitor_price_per_minute*60,2)} \\text{ per hour} \\]</p>\n<h4>c)</h4>\n<p>{name} should choose the method with the lowest cost per hour, which is {best_method}.</p>", "statement": "<p>{name} has been tasked with booking a room for a {hours}-hour meeting.</p>", "variablesTest": {"condition": "", "maxRuns": "100"}, "functions": {"pounds": {"type": "string", "parameters": [["n", "number"]], "definition": "currency(n,\"\u00a3\",\"p\")", "language": "jme"}}, "variables": {"pronouns": {"templateType": "anything", "definition": "person['pronouns']", "name": "pronouns", "group": "Person", "description": ""}, "marking_matrix": {"templateType": "anything", "definition": "let(best,min(prices),\n  map(if(x=best,1,0),x,prices)\n)", "name": "marking_matrix", "group": "Ungrouped variables", "description": "<p>Marking matrix for the \"which method is best\" part.</p>"}, "hours": {"templateType": "anything", "definition": "random(2..6)", "name": "hours", "group": "Ungrouped variables", "description": "<p>Length of the meeting in hours</p>"}, "person": {"templateType": "anything", "definition": "random_person()", "name": "person", "group": "Person", "description": ""}, "single_price_per_hour": {"templateType": "anything", "definition": "block_price_per_hour+random(0.5..2#0.25)*random(-1,1)", "name": "single_price_per_hour", "group": "Ungrouped variables", "description": "<p>Pay-as-you-go price at ACME, in pounds per hour</p>"}, "prices": {"templateType": "anything", "definition": "[block_price_per_hour,single_price_per_hour,60*competitor_price_per_minute]", "name": "prices", "group": "Ungrouped variables", "description": ""}, "block_price_per_hour": {"templateType": "anything", "definition": "random(10..25#0.25)", "name": "block_price_per_hour", "group": "Ungrouped variables", "description": "<p>Price of&nbsp;booking the room at ACME in advance, in pounds per hour</p>"}, "best_method": {"templateType": "anything", "definition": "switch(\n  min(prices)=block_price_per_hour,\n    'paying in advance at ACME',\n  min(prices)=single_price_per_hour,\n    'pay-as-you-go at ACME',\n    'paying per minute at RoomCo'\n)", "name": "best_method", "group": "Ungrouped variables", "description": "<p>A description of the cheapest method.</p>"}, "name": {"templateType": "anything", "definition": "person['name']", "name": "name", "group": "Person", "description": ""}, "verbs": {"templateType": "anything", "definition": "if(person['gender']='neutral','','s')", "name": "verbs", "group": "Person", "description": ""}, "competitor_price_per_minute": {"templateType": "anything", "definition": "floor(100*block_price_per_hour/60*(1+random(0.1..0.3#0)*random(-1,1)))/100", "name": "competitor_price_per_minute", "group": "Ungrouped variables", "description": "<p>Price of booking at RoomCo, the competitor, in pounds per minute</p>"}}, "ungrouped_variables": ["hours", "block_price_per_hour", "single_price_per_hour", "competitor_price_per_minute", "marking_matrix", "prices", "best_method"], "extensions": ["random_person"], "variable_groups": [{"name": "Person", "variables": ["person", "pronouns", "name", "verbs"]}], "rulesets": {}, "name": "David's copy of Using compound units - room hire price per hour and per minute", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Given the cost of hiring a room for a given number of hours, compare with competing prices given per hour and per minute.</p>"}, "preamble": {"css": "", "js": ""}, "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "David Rickard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/451/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "David Rickard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/451/"}]}