In this question, we will look at calculating percentage increases and decreases. We start off with some purely numerical examples before moving onto some applied situations.
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", "licence": "All rights reserved"}, "functions": {}, "rulesets": {}, "parts": [{"extendBaseMarkingAlgorithm": true, "prompt": "Increasing the quantity 100 by {incperc}% gives [[0]]
\nDecreasing the quantity 100 by {decperc}% gives [[1]]
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\nDecreasing the quantity {numtochange} by {decperc}% gives [[1]]
", "type": "gapfill", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "scripts": {}, "showCorrectAnswer": true, "gaps": [{"extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "precisionPartialCredit": 0, "showPrecisionHint": true, "correctAnswerStyle": "plain", "allowFractions": false, "unitTests": [], "marks": 1, "showFeedbackIcon": true, "precision": "2", "type": "numberentry", "variableReplacements": [], "minValue": "{numtochange}*(1+{incperc}/100)", "precisionType": "dp", "showCorrectAnswer": true, "strictPrecision": false, "customMarkingAlgorithm": "", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{numtochange}*(1+{incperc}/100)", "scripts": {}, "mustBeReducedPC": 0, "correctAnswerFraction": false}, {"extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "precisionPartialCredit": 0, "showPrecisionHint": true, "correctAnswerStyle": "plain", "allowFractions": false, "unitTests": [], "marks": 1, "showFeedbackIcon": true, "precision": "2", "type": "numberentry", "variableReplacements": [], "minValue": "{numtochange}*(1-{decperc}/100)", "precisionType": "dp", "showCorrectAnswer": true, "strictPrecision": false, "customMarkingAlgorithm": "", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{numtochange}*(1-{decperc}/100)", "scripts": {}, "mustBeReducedPC": 0, "correctAnswerFraction": false}], "customMarkingAlgorithm": "", "unitTests": [], "marks": 0, "showFeedbackIcon": true}, {"extendBaseMarkingAlgorithm": true, "prompt": "A product is not selling well at its current price of \\${price}, so the manager decides to mark down the price by {markdown}%. The mark down amounts to [[0]]
\nThe resulting sale price will then be [[1]]
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\nTo increase the quantity 100 by {incperc}%, we first need to find what {incperc}% of 100 is, then we add that value to 100. To find {incperc}% of 100, we multiply 100 by the decimal form of {incperc}. That is
\n\\[100\\times \\var{incperc}/100\\]
\nThen we add this to 100, giving
\n\\[100+100\\times \\var{incperc}/100=\\var{incpercans}.\\]
\nTo decrease the quantity 100 by {decperc}%, we first need to find what {decperc}% of 100 is, then we subtract that value from 100. To find {decperc}% of 100, we multiply 100 by the decimal form of {decperc}. That is
\n\\[100\\times \\var{decperc}/100\\]
\nThen we subtract this from 100, giving
\n\\[100-100\\times \\var{decperc}/100=\\var{decpercans}.\\]
\n\nPart b)
\nSimilarly to part a), we need to find {incperc}% and {decperc}% of {numtochange}, then add/subtract appropriately. We have
\n\\[\\var{numtochange}+\\var{numtochange}\\times \\var{incperc}/100=\\var{incpercrandans}.\\]
\n\\[\\var{numtochange}-\\var{numtochange}\\times \\var{decperc}/100=\\var{decpercrandans}.\\]
\n\nPart c)
\nTo find the markdown, we are finding the percentage {markdown}% of the original price. So we multiply {price} by the decimal form of {markdown}%. That is
\n\\[\\var{price}\\times \\var{markdown}/100=\\var{amtmarkdown}.\\]
\nThe resulting sale price is the original price, minus this markdown amount. This is the same as the percentage decrease problems in part a) and b).
\n\\[\\var{price}-\\var{price}\\times \\var{markdown}/100=\\var{markdownprice}.\\]
\n\nPart d)
\nIn this problem, the meal price (which includes the tax) could be thought of as 110% of the tax-free meal price. So to find the tax (which is 10% of the tax-free meal price), one way is to find 1% of the full price and then multiply by 10. This is kind of like the unit cost method in a way. So we have
\n\\[\\frac{\\var{mealcost}}{110}\\times 10=\\var{mealtax}.\\]
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", "group": "Ungrouped variables", "templateType": "randrange"}}, "type": "question"}, {"name": "Compare prices and values using the unit cost method", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Dann Mallet", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/800/"}], "metadata": {"description": "", "licence": "All rights reserved"}, "preamble": {"css": "", "js": ""}, "advice": "We have two different prices: the pre-packaged price is given for a decimal quantity of kg, while the loose price is in kg. If we are to compare prices using prices per kg, the loose price is already in the correct form, but we need to convert the pre-packaged price to a price for 1kg. So we need to divide the pre-packaged price by that decimal quantity to give the unit price in \\$/kg. Once that value is known, we compare it directly with the price per kilogram to buy at the loose produce price.
", "tags": [], "functions": {}, "parts": [{"stepsPenalty": 0, "marks": 0, "variableReplacements": [], "unitTests": [], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "type": "information", "prompt": "At a local produce market, {fruit} are sold pre-packaged or loosely. You can buy {fruit} in {packsize}kg pre-packaged bags for \\${packprice} or loosely for \\${looseprice} per kg. Use the unit cost method to decide which is the best value for money.
", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "scripts": {}, "steps": [{"notationStyles": ["plain", "en", "si-en"], "marks": 1, "correctAnswerStyle": "plain", "mustBeReduced": false, "variableReplacements": [], "unitTests": [], "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "correctAnswerFraction": false, "allowFractions": false, "type": "numberentry", "prompt": "If the unit to compare is kilograms, then the unit cost for the pre-packaged {fruit} in \\$/kg is
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", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "scripts": {}, "minMarks": 0, "showCellAnswerState": true, "variableReplacementStrategy": "originalfirst"}], "variableReplacementStrategy": "originalfirst"}], "rulesets": {}, "ungrouped_variables": ["fruit", "packsize", "packprice", "looseprice"], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"packprice": {"templateType": "randrange", "description": "", "group": "Ungrouped variables", "definition": "random(2..8#0.34)", "name": "packprice"}, "fruit": {"templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random('apples','bananas','oranges','potatoes','tomatoes')", "name": "fruit"}, "packsize": {"templateType": "randrange", "description": "", "group": "Ungrouped variables", "definition": "random(0.25..0.8#0.05)", "name": "packsize"}, "looseprice": {"templateType": "randrange", "description": "", "group": "Ungrouped variables", "definition": "random(5..18#0.37)", "name": "looseprice"}}, "variable_groups": [], "statement": "The unit cost method is a way of comparing the price or value of two or more things when those prices or values do NOT refer to the same quantity. For example, we might want to know whether it's better to buy a 750g bag of apples priced at \\$5, or to buy loose apples at \\$5.50 per kg.
\nThe method involves
\n