Project 5 QR Percentages Version A Cherokee Williams

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Eastern Gateway Community College *

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105

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Economics

Date

Feb 20, 2024

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docx

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Incorrect Percentages(A) Name: Cherokee Williams 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 "Apple spends far less on Research & Development than any of its rivals". • Why is that assumption incorrect? It assumes that the companies make the same revenue when in fact 2% of Apples revenue can be more than 14% of Google or Microsoft. • Is there a situation where the headline is still correct? The best way to fix the headline is to use dollar amounts instead of percentages, this gives a more accurate and correct analysis of how much each company spends on Research and Development. • 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 mistake is that the percentage increase and the percentage decrease are both determined using the initial price of $100 price as the basis for each the initial mark-up and subsequent mark-dow • Why is that assumption incorrect? The 50% reduction is off of the new shoes price after the raise in price, which is now $150. • What do the shoes actually cost now? Initial price was raised from $100 to $150; then decreased to thefinal price of $75 • By what percent should the shoes be decreased in order to have the price back at $150? % decrease = (150-100)/150 = 0.3333 or 33.33% If the interim price of $150 was decreased by 33.33 % then the price would be back at $100. • 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 assumption is that the burglaries percentages are compared to the same year, when in fact the comparison is compared to the previous year. The number of burglaries changed.

• By what percent has the number of burglaries actually changed in the two- year period? As shown in past B, the actual number of burglaries over the 2-year period is 98 burglaries.This is a change of 2 out of the total of 100 burglaries.By definition of percent, 2 out of 100 is 2%. % Change = 2/100 = 0.02 or a 2% decrease. • 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? As shown above in part b, a 10% increase over 2-years (using a basis of 100 burglaries) would be 110 burglaries. Burglaries end of 2013 = 140 * X 110 = 140X 110/140 = 140X/140 110/140 = X .7857 = X 1-.7857 = 21.43% decrease A 21.43% decrease in the 2ndyear would yield a net 10% decrease over the 2-year period, given the facts of this problem. • 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 shopkeeper's mistaken assumption is that the both the discounts are being given on the same starting price (basis). But there are 2 steps to this calculation and a different basis in each step (basis for step 2 is the ending figure of step 1). • Why is that assumption incorrect? In actuality, the step one 60%-reduction is calculated using the basis of the total price of the goods before discount (100 - (100*.6); and in a second step the additional 20% is taken off the figure that resulted in step one. Final price = 100 - ((100*.6) *.8) If you did truly have 80% discount, explain what should happen when you go to the counter to buy $500 worth of items? You would only pay 20% of 500 or $100 for the goods. FINAL PRICE = $500 - (500*.8)OR THE FINAL PRICE = $500 - $400OR FINAL PRICE = $100 • If you got your 60% discount and opened the card for an additional 20%, what is the actual % discount you would receive? • Is it better to apply the 60% discount first or the 20% discount first? It does not matter which way you do it, it comes out to the same price for this problem ($32.00).

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