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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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A small sequence of questions on calculating percentage increases and decreases. Moving from percentages of 100, to percentages of some random whole number, and onto calculating percentage changes in applied financial situations.

Increasing the quantity 100 by {incperc}% gives [[0]]

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Decreasing the quantity 100 by {decperc}% gives [[1]]

Increasing the quantity {numtochange} by {incperc}% gives [[0]]

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Decreasing the quantity {numtochange} by {decperc}% gives [[1]]

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]] \n The resulting sale price will then be [[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": "{markdown}/100*{price}", "precisionType": "dp", "showCorrectAnswer": true, "strictPrecision": false, "customMarkingAlgorithm": "", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{markdown}/100*{price}", "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": "{price}*(1-{markdown}/100)", "precisionType": "dp", "showCorrectAnswer": true, "strictPrecision": false, "customMarkingAlgorithm": "", "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{price}*(1-{markdown}/100)", "scripts": {}, "mustBeReducedPC": 0, "correctAnswerFraction": false}], "customMarkingAlgorithm": "", "unitTests": [], "marks": 0, "showFeedbackIcon": true}, {"extendBaseMarkingAlgorithm": true, "prompt": " Australia has a 10% goods and services tax. Generally, the price that you see marked on a product or in a menu includes the tax. If the price of a meal at Euler's Eatery comes to \\${mealcost}, then the amount of tax included in the price is [[0]]

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Part a)

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To 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

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\$100\\times \\var{incperc}/100\$

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Then we add this to 100, giving

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\$100+100\\times \\var{incperc}/100=\\var{incpercans}.\$

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To 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

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\$100\\times \\var{decperc}/100\$

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Then we subtract this from 100, giving

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\$100-100\\times \\var{decperc}/100=\\var{decpercans}.\$

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Part b)

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Similarly to part a), we need to find {incperc}% and {decperc}% of {numtochange}, then add/subtract appropriately. We have

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\$\\var{numtochange}+\\var{numtochange}\\times \\var{incperc}/100=\\var{incpercrandans}.\$

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\$\\var{numtochange}-\\var{numtochange}\\times \\var{decperc}/100=\\var{decpercrandans}.\$

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Part c)

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To 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

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\$\\var{price}\\times \\var{markdown}/100=\\var{amtmarkdown}.\$

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The 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).

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\$\\var{price}-\\var{price}\\times \\var{markdown}/100=\\var{markdownprice}.\$

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Part d)

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In 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

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\$\\frac{\\var{mealcost}}{110}\\times 10=\\var{mealtax}.\$

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Decrease percentage

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Answer to the increase percentage question

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Answer to the decrease percentage question

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Increase percentage

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The value to be changed by some percentage

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