Math CentralQuandaries & Queries


Question from Suszanne, a teacher:

Mary purchased an item for 45% off the original price, plus an additional 20% off the sale price. She also had a $\$5$ off coupon, which the salesclerk applied after these two discounts. Mary's final purchase price for the item was $\$50.$ She paid no sales tax, what was the original price of the item?

Hi Suszanne,

Suppose the original price was $\$P.$ The first sale was 45% off so after this was applied she would pay 55% of the original price. Thus the sale price was $0.55 \times \$P.$ The additional reduction was 20% of this so she was to pay 80% of the sale price. How much is this? From this amount subtract $\$5$ and you get $\$50.$ Solve for $P.$


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