Question

一道GMAT数学题

This year Henry will save a certain amount of his
income, and he will spend the rest. Next year Henry
will have no income, but for each dollar that he saves
this year, he will have 1 + r dollars available to spend.
In terms of r, what fraction of his income should Henry
save this year so that next year the amount he has
available to spend will be equal to half the amount that
he spends this year?

for each dollar that he saves
this year, he will have 1 + r dollars available to spend.
完全不懂这句话……求解！

Answer 1

他今年每省下一美元，明年他就会有1+r个美元。比如今年总共省了50美元，明年他的总财产就会有50×（1+r）个。

这题的意思，我要没理解错，这么解：
设所求的比例为x(即今年省下的钱的比例)，今年的总财产为M。
那么按题就有xM（1+r）=（1/2）(1-x)M
x=1/(3+2r)

以上个人理解，错了勿怪-_-|

Answer 2

设今年存了x花了y
则明年取出来x（1+r）
令x（1+r）=y/2则得出y=2x（1+r）

要求的fraction=x/x+y=x/x(2r+3)=1/2r+3