GMAT
题目
Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?
解析
这里是一种解题思路。
设 \(M\) = 爱丽丝每月实得工资
设 \(f\) = 用于计算每月储蓄的比例
这意味着 \(fM\) = 爱丽丝每月储蓄的金额
同时这也意味着她的**年度储蓄** = \(12fM\)
重要提示：如果 \(f\) 是用于计算每月**储蓄**的比例，那么 \(1-f\) 就是用于计算**未储蓄**金额的比例
这意味着 \((1-f)M\) = 爱丽丝每月**未储蓄**的金额
现在我们可以列方程了。
她年底存下的总金额是她每月实得工资中**未储蓄部分**的3倍。
我们得到：
\[
12fM = 3(1-f)M
\]
现在求解 \(f\)：
展开得：
\[
12fM = 3M - 3fM
\]
化简：
\[
15fM = 3M
\]
两边同时除以 \(15M\) 得：
\[
f = \frac{3M}{15M} = \frac{1}{5}
\]
答案：D
在线客服
官方微信
公众号