// Numbas version: finer_feedback_settings
{"name": "Percentage question 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Percentage question 2", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>We often need to work out a particular % of a weight, volume or number of, for example, tablets, days etc. If you understand the basic concept and simple alegebra this should not be too tricky.</p>\n<p>Answer the following three question parts. Please enter your answers as a decimal, not a fraction. Give your answer to two decimal places (only round your final answer, use the exact values on your calculator when working out any intermediate steps).</p>\n<p>If you would like to see how to do this question, click on 'Reveal answers' at the bottom of the page.</p>", "advice": "<p>Remember percentage (%) means part per 100 so can be considerd as a fraction out of a hundred. You could imagine 70% as the fraction 70/100 (also written $ \\frac{70}{100} $ ) or as the decimal 0.7 out of 1.</p>\n<p>For the fraction $ \\frac{70}{100} $. In maths we call the top part of the fraction (70) the <strong>numerator</strong>. We call the bottom part (100) the <strong>denominator</strong>. When working out division sums you need to be sure you use the correct numbers for the numerator and denominator otherwise your answer will be wrong.</p>\n<p><strong><span style=\"text-decoration: underline;\">Rounding</span>.</strong>&nbsp;You need to make sure you know how to round answers to two decimal places. Look at your answer and locate the second and third digits after the decimal place.</p>\n<ul>\n<li>If the third digit is 0, 1, 2, 3 or 4 you just keep the second digit the same and discard any digits after the second. For example 34.1702 is rounded to two decimal places as 34.17 as <span style=\"text-decoration: underline;\"><strong>0</strong></span> is the third digit after the decimal place</li>\n<li>If the third digit is 5, 6, 7, 8 or 9 add one to the second digit and discard any digits after the second. For example 34.1751 is rounded to two decimal places as 34.18 as <span style=\"text-decoration: underline;\"><strong>5</strong></span> is the third digit after the decimal place</li>\n</ul>\n<p><span style=\"text-decoration: underline;\"><strong>Part a</strong></span></p>\n<p>You can use simple algebra to work this out. We can call the answer $y$ and as we know that a % is really a fraction of 100 we can write the following equation</p>\n<p>$ \\frac{\\var{percentage}}{\\var{number}} = \\frac{y}{100} $</p>\n<p>If we multiply both sides of the equation by a hundred (<em>equivalent to moving 100 from a division on the right of the equation to a multiplication on the left</em>) we have the equation</p>\n<p>$ 100 \\times \\frac{\\var{percentage}}{\\var{number}} = y $</p>\n<p>Don't forget to round your answer to two decimal places</p>\n<p style=\"padding-left: 40px;\"><span style=\"text-decoration: underline;\"><strong>Part b</strong></span></p>\n<p style=\"padding-left: 40px;\">We can call the answer $z$ and as we know that a % is really a fraction of 100 we can write the following equation</p>\n<p style=\"padding-left: 40px;\">$ \\frac{\\var{answer}}{z} = \\frac{\\var{percentage}}{100} $</p>\n<p style=\"padding-left: 40px;\">We can rearrange this equation by multiplying both sides of the equation by 100 to get</p>\n<p style=\"padding-left: 40px;\">$ 100 \\times \\frac{\\var{answer}}{z}&nbsp; = \\var{percentage} $</p>\n<p style=\"padding-left: 40px;\">We then multiply both sides by z to get&nbsp;</p>\n<p style=\"padding-left: 40px;\">$ 100 \\times \\var{answer} = \\var{percentage} \\times z $</p>\n<p style=\"padding-left: 40px;\">To get z we just divide both sides by {percentage}</p>\n<p style=\"padding-left: 40px;\">$ 100 \\times \\frac{\\var{answer}}{\\var{percentage}} = z $</p>\n<p><span style=\"text-decoration: underline;\"><strong>Part c</strong></span></p>\n<p>Imagine the number is $w$. If we increase this by $ \\var{percentage}%$ we get $w \\times (100 + {\\var{percentage}})$&nbsp;</p>\n<p>We can convert this to a percentage with $w \\times (100 + {\\var{percentage}})$ as numerator and 100 as denominator.</p>\n<p>We know this is percentage is $ \\var{number}$ so we can write the equation</p>\n<p>$\\frac{w \\times (100 + {\\var{percentage}})}{100} = \\var{number}$</p>\n<p>We can rearrange the eqution so&nbsp;</p>\n<p>$w= 100 \\times \\frac{\\var{number}}{(100 + {\\var{percentage}})}$</p>\n<p></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"percentage": {"name": "percentage", "group": "Ungrouped variables", "definition": "random(8 .. 50#1)", "description": "<p>This is the perecentage</p>", "templateType": "randrange", "can_override": false}, "number": {"name": "number", "group": "Ungrouped variables", "definition": "random(52 .. 100#1)", "description": "", "templateType": "randrange", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "random(1 .. 25#1)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["percentage", "number", "answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is {percentage}% of {number}?</p>", "minValue": "{percentage}*{number}/100", "maxValue": "{percentage}*{number}/100", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct number of decimal places.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The number {answer} is {percentage}% of what number?</p>", "minValue": "100*{answer}/{percentage}", "maxValue": "100*{answer}/{percentage}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A number is increased by {percentage}% to make the number {number}. 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