Emily has a coupon of 20 % off for her purchase at the store. She finds a backpack that she likes on the discount rack. Its original price is $60 but everything in the rack comes with a 30 % discount. Emily says “Thirty percent and twenty percent make fifty percent so it will cost $30”. Is Emily correct? Explain by finding the price which Emily will pay for the backpack.
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It is true that 20% and 30% make 50%. But in the context of sale prices it is essential to keep track of the wholes to which these percents apply. For the backpack, the 30% discount applies to the original $60 price: 30% of $60 is 0.3×60=18 making the discount on the backback $18. So after using the coupon, the backpack price becomes $42. Emily's additional 20% coupon applies not to the original backpack price but to the discounted price of $42: 20% of $42 is $8.40. Emily would need to save an additional $12 off the $42 price in order to buy the backpack for $30 so her calculations are not correct.
(b).As seen in part (a), Emily's coupon lowers the discount rack price by $8.40 so she will pay
42−8.40=33.60
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