2005 AMC 8 第 11 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
11.
伯格维尔的销售税率为 。伯格维尔大衣店促销期间，一件原价为 的外套打 折扣。两名店员杰克和吉尔各自计算账单。杰克先按 加收 的销售税，再从总额中减去 。吉尔先从 中减去原价的 ，再对折后价加收 的销售税。杰克的总额减去吉尔的总额是多少？
The sales tax rate in Bergville is . During a sale at the Bergville Coat Closet, the price of a coat is discounted from its price. Two clerks, Jack and Jill, calculate the bill independently. Jack rings up and adds sales tax, then subtracts from this total. Jill rings up , subtracts of the price, then adds of the discounted price for sales tax. What is Jack’s total minus Jill’s total?
答案：C
小提示：
加税和打折都是乘法
Adding tax and taking the discount are both multiplications.
大提示：
乘法顺序不同结果相同
Multiplication gives the same result in either order.
解答：
杰克的总额是 美元。
吉尔的总额是 美元。
因为乘法满足交换律，这两个乘积相等，所以杰克的总额减去吉尔的总额为 。
所以正确答案是 C。
Jack’s total is dollars.
Jill’s total is dollars.
These products are equal because multiplication is commutative, so Jack’s total minus Jill’s total is .
Thus, C is the correct answer.
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