// Numbas version: exam_results_page_options
{"name": "Ugur's copy of Percentages and ratios - box of chocolates", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Ugur's copy of Percentages and ratios - box of chocolates", "tags": [], "metadata": {"description": "<p>A simple situational question about a box of chocolates, asking how many of each type there are, what percentage of the box they represent, the probability of picking one and ratios of different types.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p></p>", "advice": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<h4><strong>a)</strong></h4>\n<p>100% represents the whole box of chocolates. As there are 5 different kinds of chocolate in the box and they are all represented equally, to calculate the percentage chocolates which are caramel, divide 100 by 5.</p>\n<p style=\"text-align: center;\">Caramel chocolate = $\\displaystyle\\frac{100}{5}$ = $20$% of the box.</p>\n<p></p>\n<p></p>\n<p><strong>b)</strong>&nbsp;</p>\n<p>The original number of chocolates&nbsp;in the box is stated. We worked out above that each type of chocolate makes up 20% of the box, so we need to work out 20% of {chocs}.</p>\n<p>To do this, either divide {chocs} by 100 and multiply by 20, OR multiply {chocs} by 0.2. The two methods will give the same result.</p>\n<p style=\"text-align: center;\">Method 1: $\\displaystyle\\frac{\\var{chocs}}{100}$ x $20$&nbsp;= $\\var{type}$;</p>\n<p style=\"text-align: center;\"><strong>OR</strong></p>\n<p style=\"text-align: center;\">Method 2: $\\var{chocs}$ x $0.2$ = $\\var{type}$.</p>\n<p></p>\n<p></p>\n<p><strong>c)</strong></p>\n<p>There are now {type} fewer chocolates in the box, but the remaining chocolates&nbsp;now represent 100% of the box. There are now only 4 types of chocolate in it and there is still equal representation inside the box.</p>\n<p>Use the method from part <strong>a)</strong> to find out the equal share of each chocolate type.</p>\n<p style=\"text-align: center;\">Each type = $\\displaystyle\\frac{100}{4}$ = $25$% of the box.</p>\n<p></p>\n<p></p>\n<p><strong>d)</strong>&nbsp;</p>\n<p><em>i)</em></p>\n<p>The first section asks you to compare plain chocolate and dark chocolate. It states that there are {p} plain chocolates and {d} dark chocolates left in the box.</p>\n<p>Insert the numbers of each into the gaps.</p>\n<p style=\"text-align: center;\">Plain $\\var{p}$ : $\\var{d}$ Dark</p>\n<p style=\"text-align: left;\">From this, we should look to see if this answer can be simplified down. To do this, we need to find the greatest common divisor of $\\var{p}$ and&nbsp;$\\var{d}$.&nbsp;</p>\n<p style=\"text-align: left;\">The greatest common divisor is $\\var{gcd}$.</p>\n<p style=\"text-align: left;\"><span data-jme-visible=\"gcd&gt;1\">Using this value to simplify down the ratio by dividing each term by the value, the final answer is</span></p>\n<p style=\"text-align: center;\"><span data-jme-visible=\"gcd&gt;1\">Plain $\\var{ratio_plain}$ : $\\var{ratio_dark}$ Dark.</span></p>\n<p><span data-jme-visible=\"gcd&gt;1\">This states that for every {ratio_plain} plain {if(ratio_plain=1,\"chocolate\",\"chocolates\")}, there {if(ratio_dark=1,\"is\",\"are\")} {ratio_dark} dark {if(ratio_dark=1,\"chocolate\",\"chocolates\")}.</span></p>\n<p><span data-jme-visible=\"gcd=1\">Therefore, it is not possible to simplify further and the final answer is</span></p>\n<p style=\"text-align: center;\"><span data-jme-visible=\"gcd=1\">Plain $\\var{p}$ : $\\var{d}$ Dark.</span></p>\n<p><span data-jme-visible=\"gcd=1\">This states that for every {p} plain {if(p=1,\"chocolate\",\"chocolates\")}, there {if(d=1,\"is\",\"are\")}{d} dark {if(d=1,\"chocolate\",\"chocolates\")}.</span></p>\n<p></p>\n<p><em>ii)</em></p>\n<p>The second section asks you to compare coconut chocolates and the rest of the box. It states that there are {c} coconut chocolates. To calculate the number of chocolates in the rest of the box, add together the stated amounts of plain, dark and nutty chocolates:</p>\n<p style=\"text-align: center;\">$\\var{p}+\\var{d}+\\var{n}$ = $\\var{rob}$.</p>\n<p>Insert these two figures into the gaps.</p>\n<p style=\"text-align: center;\">Coconut $\\var{c}$ : $\\var{rob}$ Other chocolates</p>\n<p style=\"text-align: left;\">From this, we should look to see if this answer can be simplified down. To do this, we need to find the greatest common divisor of $\\var{c}$ and&nbsp;$\\var{rob}$.&nbsp;</p>\n<p style=\"text-align: left;\">The greatest common divisor is $\\var{gcd2}$.</p>\n<p style=\"text-align: left;\"><span data-jme-visible=\"gcd2 &gt; 1\">Using this value to simplify down the ratio by dividing each term by the value, the final answer is</span></p>\n<p style=\"text-align: center;\"><span data-jme-visible=\"gcd2 &gt; 1\">Coconut $\\var{ratio_coconut}$ : $\\var{ratio_rest}$ Other chocolates.</span></p>\n<p><span data-jme-visible=\"gcd2 &gt; 1\">This states that for every {ratio_coconut} coconut {if(ratio_coconut=1,\"chocolate\",\"chocolates\")}, there {if(ratio_rest=1,\"is\",\"are\")} {ratio_rest} other {if(ratio_rest=1,\"chocolate\",\"chocolates\")} in the box.</span></p>\n<p><strong></strong><span data-jme-visible=\"gcd2 = 1\">Therefore, it is not possible to simplify further and the final answer is&nbsp;</span></p>\n<p style=\"text-align: center;\"><span data-jme-visible=\"gcd2 = 1\">Coconut $\\var{c}$ : $\\var{rob}$ Other chocolates.</span></p>\n<p style=\"text-align: left;\"><span data-jme-visible=\"gcd2 = 1\">This states that for every {c} coconut {if(c=1,\"chocolate\",\"chocolates\")}, there {if(rob=1,\"is\",\"are\")} {rob} other {if(rob=1,\"chocolate\",\"chocolates\")} in the box.</span></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"ratio_dark": {"name": "ratio_dark", "group": "Ungrouped variables", "definition": "d/gcd(p,d)", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>Number of dark chocolates in ratio of plain to dark.</p>", "templateType": "anything", "can_override": false}, "prob": {"name": "prob", "group": "Ungrouped variables", "definition": "precround({n/{a},2)", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>Probability that a nutty chocolate is selected from the box on day 3.</p>", "templateType": "anything", "can_override": false}, "type": {"name": "type", "group": "Ungrouped variables", "definition": "chocs/5", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>Number of each type of chocolate in the box initially.</p>", "templateType": "anything", "can_override": false}, "minusc": {"name": "minusc", "group": "Ungrouped variables", "definition": "{chocs-type}", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>Number of chocolates in the box minus caramel.</p>", "templateType": "anything", "can_override": false}, "chocs": {"name": "chocs", "group": "Ungrouped variables", "definition": "random(70 .. 95#5)", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>Total number of chocolates in the box before eating.</p>", "templateType": "randrange", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "p+n+d+c", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>Number of chocolates in the box on day 3.</p>", "templateType": "anything", "can_override": false}, "gcd2": {"name": "gcd2", "group": "Ungrouped variables", "definition": "gcd(c,rob)", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p></p>", "templateType": "anything", "can_override": false}, "perc": {"name": "perc", "group": "Ungrouped variables", "definition": "100*(prob)", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>Percentage version of probability.</p>", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(1..14 except 7 except 11 except 13)", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>Number of nutty chocolates on day 3.</p>", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(1..3)*p", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>Number of dark chocolates on day 3.</p>", "templateType": "anything", "can_override": false}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>Number of plain chocolates on day 3.</p>", "templateType": "anything", "can_override": false}, "ratio_coconut": {"name": "ratio_coconut", "group": "Ungrouped variables", "definition": "c/gcd(c, rob)", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>Number of coconut chocolates in ratio of coconut&nbsp;to rest of box.</p>", "templateType": "anything", "can_override": false}, "ratio_plain": {"name": "ratio_plain", "group": "Ungrouped variables", "definition": "p/gcd(p,d)", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>Number of plain chocolates in ratio of plain to dark.</p>", "templateType": "anything", "can_override": false}, "rob": {"name": "rob", "group": "Ungrouped variables", "definition": "p+n+d", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>Sum of the rest of the box excluding coconut.</p>", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1..14 except 7 except 11 except 13)", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>Number of coconut chocolates on day 3.</p>", "templateType": "anything", "can_override": false}, "ratio_rest": {"name": "ratio_rest", "group": "Ungrouped variables", "definition": "rob/gcd(c, rob)", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>Number of 'rest of box' chocolates in ratio of coconut&nbsp;to rest of box.</p>", "templateType": "anything", "can_override": false}, "gcd": {"name": "gcd", "group": "Ungrouped variables", "definition": "gcd(p,d)", "description": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p></p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["chocs", "type", "p", "n", "d", "c", "rob", "prob", "a", "perc", "minusc", "ratio_plain", "ratio_dark", "ratio_coconut", "ratio_rest", "gcd", "gcd2"], "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": "<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<div id=\"MathJax_Message\" style=\"display: none;\"></div>\n<p>A family receive a box of chocolates as a gift. There are five different kinds of chocolate inside, plain, nut, caramel, dark and coconut.</p>\n<p>There are:</p>\n<p>$\\var{p}$&nbsp;plain chocolates,&nbsp;$\\var{n}$ nutty chocolates,&nbsp;$\\var{c}$ coconut chocolates and&nbsp;$\\var{d}$ dark chocolates.</p>\n<p></p>\n<p><em>i) What is the probability of picking a plain chocolate&nbsp;</em></p>\n<p>[[0]] Give your answer as fraction!</p>\n<p></p>\n<p><em>ii)&nbsp;</em>What is the probablity of picking a coconut chocolate.</p>\n<p>[[1]] Give your answer as fraction!</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Gap 0.", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{p}/{p+n+d+c}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{c}/{p+n+c+d}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}, {"name": "Ugur Efem", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14200/"}]}]}], "contributors": [{"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Adelle Colbourn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2083/"}, {"name": "Ugur Efem", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14200/"}]}