AMC12 2008 A

AMC12 2008 A · Q6

AMC12 2008 A · Q6. It mainly tests Linear equations, Percent.

Heather compares the price of a new computer at two different stores. Store $A$ offers $15\%$ off the sticker price followed by a $\$90$ rebate, and store $B$ offers $25\%$ off the same sticker price with no rebate. Heather saves $\$15$ by buying the computer at store $A$ instead of store $B$. What is the sticker price of the computer, in dollars?

Heather 在两家不同的商店比较一台新电脑的价格。A 店先在标价基础上打 $15\%$ 折扣，然后再返还 $\$90$；B 店对相同标价打 $25\%$ 折扣，但没有返现。Heather 在 A 店购买比在 B 店购买节省了 $\$15$。这台电脑的标价是多少美元？

(A) 750 750

(B) 900 900

(D) 1050 1050

(E) 1500 1500

Answer

Correct choice: (A)

正确答案：（A）

Solution

Let the sticker price be $x$. The price of the computer is $0.85x-90$ at store $A$ and $0.75x$ at store $B$. Heather saves $\$15$ at store $A$, so $0.85x-90+15=0.75x$. Solving, we find $x=750$, and thus the answer is $\mathrm{(A)}$. The $\$ 90$ at store $A$ is $\$ 15$ greater than the additional $25\%-15\% = 10\%$ off at store $B$. Thus the $10\%$ off is equal to $\$ 90$ $-$ $\$ 15$ $=$ $\$ 75$, and therefore the sticker price is $\$ 750$.

设标价为 $x$。在 A 店的价格为 $0.85x-90$，在 B 店的价格为 $0.75x$。 Heather 在 A 店节省 $\$15$，所以 $0.85x-90+15=0.75x$。解得 $x=750$，因此答案是 $\mathrm{(A)}$。 A 店的 $\$ 90$ 比 B 店额外的 $25\%-15\% = 10\%$ 折扣多 $\$ 15$。因此这 $10\%$ 折扣等于 $\$ 90$ $-$ $\$ 15$ $=$ $\$ 75$，所以标价为 $\$ 750$。

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