Incorrect Percentages(A)

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105

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Economics

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Jan 9, 2024

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Incorrect Percentages(A) Name: Nikole Stull Must show calculations/formula for credit. Any answer given with no calculations shown will result in no credit for that answer. A newspaper headline claims: "Apple spends far less on Research & Development than any of its rivals." Further into the story, the reporter writes that Apple spends a paltry 2% of revenues compared with 14% at Google and Microsoft. What is the mistaken assumption here? - The mistaken assumption is that they all made the same revenue. Why is that assumption incorrect? - It is not correct because we do not know how much each company made. All we know is the revenue % they spent. Is there a situation where the headline is still correct? - The headline would still be correct as long as the article stated how much revenue was made and how if all the companies made the same amount. A shop owner raises the price of a $150 pair of shoes by 40%. After a few weeks, because of falling sales, the owner reduces the price of the shoes by 40%. A customer then says that the shoes are back at the original price. What is the mistaken assumption here? - The mistaken assumption is that the shoes are back at the original price. Why is that assumption incorrect? -It is incorrect because the price of the shoes would be 40% less than the increased price. What do the shoes actually cost now? show calculation. - 150(1.4) =210 - 210(1-0.4) =126. - The shoes cost $126 By what percent should the shoes be decreased in order to have the price back at $150? Round to the nearest 10th percentage. (for example if your decimal answer is .058267 your answer would be 5.8267% round to nearest 10th percent answer is 5.8%) show calculation - 210x=150, 150/210 = 0.71428 - 0.71428(100) = 71.4%

- 1-.714= 0.286 - 0.286(100) = 28.6%. - The shoes needed to be reduced by 28.6% to cost $150 again The annual number of burglaries in a town rose by 50% in 2012 and fell by 10% in 2013. Hence the total number of burglaries increased by 40% over the two- year period. What is the mistaken assumption here? - The mistaken assumption is that the crime rate only rose by 40% over the course of two years. Why is that assumption incorrect? - That assumption is incorrect because the crime rate rose 50% the first year and 40% the second year. By what percent has the number of burglaries actually changed in the two-year period? show calculation - 100(1.5) = 150 burglaries in 2012 - 150(.9) = 135 burglaries in 2013 - 135-100 = 35% increase in burglaries over the two-year period By what percent would the crime have to decrease in the second year in order for the change over the two-year period to actually be a 40% increase? Round to nearest 10th percent (ex-decimal .05873 is 5.873% to one decimal is 5.9%) show calculation - 150x = 140. 140/150 = 0.93333 - 1-0.93333 = 0.06667(100) = 6.667 or 6.7% - The crime rate would have to decrease by 6.7% to be a 40% increase over the two-year period. A store is currently offering a 60% discount on all items purchased. Your cashier is trying to convince you to open a store credit card and says to you, "In addition to the 60% discount you are receiving for purchasing these items on sale today, you will get an additional 20% off for opening a credit card account. That means you are getting 80% off!" What is the mistaken assumption here? - The mistaken assumption is that you get a total of 80% off your purchase. Why is that assumption incorrect? - It is incorrect because you only get 60% off your purchase. - Opening the credit card would give you an additional 20% off the already discounted total.

If you did truly have 80% discount, explain what should happen when you go to the counter to buy $500 worth of items? show calculation - If you truly received an 80% discount off a $500 purchase, then your total would be $100. - 80% of $500 is $400. - 400- 500 = $100. If you got your 60% discount and opened the card for an additional 20%, what is the actual % discount you would receive? show calculation - X = 500(1-.6)(1-.2) = 160 - 500-160 = 340 - 340/500 = 0.68(100) = 68% - The total discount is 68% Is it better to apply the 60% discount first or the 20% discount first? show calculation - X = 500 (1-.6) = 200 - 500-200 = 300 - 300(1-.2) = 240 - X = 500 (1-.2) = 400 - 400 (1-.6) = 160 - It would be better to apply the 20% discount first, then apply the 60% discount

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