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 $\$ 10.00$. At 9:15 a.m., the price was reduced to $\$ 9.00$. As soon as the price of the carpet fell below $\$ 8.00$, Emily bought it. At what time did Emily buy the carpet?
(A) 9:45 a.m.
(B) 9:15 a.m.
(C) 9:30 a.m.
(D) 10:15 a.m.
(E) 10:00 a.m.
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 $\$ 9.00$.

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 $\$ 8.00$ at 9:45 a.m., so Emily bought the carpet at 9:45 a.m.

ANSWER: (A)

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