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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.

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

\n

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

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

\n

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}.\$

\n

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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}.\$

\n

\n

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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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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The price for purchasing {fruit} loosely is already given in terms of a price per kg. Comparing your two unit prices, select the option which provides the best value for money.

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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.

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The method involves

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\n
1. Decide on your \"unit\" of comparison
2. \n
3. Converting the prices or values to equivalents for that unit
4. \n
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