2005 CEMC Gauss (Grade 7) Problems/Problem 21

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Problem

Emily was at a garage sale where the price of every item was reduced by $10\%$ of its current price every $15$ minutes. At 9:00 a.m., the price of a carpet was $10$ dollars. At 9:15 a.m., the price was reduced to $9$ dollars. As soon as the price of the carpet fell below $8$ dollars, Emily bought it. At what time did Emily buy the carpet?

$\text{(A)}$ 9:45 a.m. $\text{(B)}$ 9:15 a.m. $\text{(C)}$ 9:30 a.m. $\text{(D)}$ 10:15 a.m. $\text{(E)}$ 10:00 a.m.

Solution

Since the price of the carpet is reduced by $10\%$ every $15$ minutes, then the price is multiplied by $0.9$ every $15$ minutes. At 9:15, the price was $9$ dollars. At 9:30, the price fell to $0.9\times 9.00 = 8.10$. At 9:45, the price fell to $0.9\times 8.10 = 7.29$. So the price fell below 8 dollars at 9:45 a.m., so Emily bought the carpet at 9:45 a.m. The answer is $A$.

See Also

2005 CEMC Gauss (Grade 7) (ProblemsAnswer KeyResources)
Preceded by
Problem 20
Followed by
Problem 22
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CEMC Gauss (Grade 7)