2005 AMC 12A 第 4 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。
4.
一家商店通常以每扇 的价格出售窗户。本周每买四扇就赠送一扇。Dave 需要七扇窗户，Doug 需要八扇窗户。如果他们合在一起购买而不是分别购买，可以节省多少美元？
A store normally sells windows at each. This week the store is offering one free window for each purchase of four. Dave needs seven windows and Doug needs eight windows. How many dollars will they save if they purchase the windows together rather than separately?
答案：A
小提示：
每付钱买 扇窗户，就免费得到第 扇。
For every windows paid for, a th comes free
大提示：
比较分别购买时需要付款的窗户数，以及合起来买 扇时需要付款的窗户数。
Compare the number of paid windows separately versus for windows together
解答：
分别购买时，Dave 买 扇需付 扇的钱，即 ；Doug 买 扇需付 扇的钱，即 ，合计 。
合起来买时共需 扇，付 扇的钱可得 扇免费，费用为 。
因此节省 。
所以正确答案是 A。
Buying separately, Dave gets windows by paying for (), and Doug gets by paying for (), for a total of
Buying together, they need windows: paying for yields free, for a cost of
The savings are
Thus, the correct answer is A.
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