[問題]GWD 27-Q19

[applepeko]

Q19:
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 was available to spend will be equal to half the amount that he spends this year?

A. 1/(r+2)
B. 1/(2r+2)
C. 1/(3r+2)
D. 1/(r+3)
E. 1/(2r+3)


答案是E,
如果假設save的錢是X, spend的錢是Y,
我算到(1+r)X=Y/2
後面就不知道了!
有人可以幫我解答一下嗎??
感激不盡 :]

[spreewell]

設今年存的錢為S，今年花的錢為P
所以明年可花的錢便為S(1+R)，依題意我們可獲得以下的式子
S(1+R) = (1/2)P
P=2S(1+R)
題目要我們求S/S+P的比例，把上式帶入
S/S+P=S/S+2S(1+R)=S/S(1+2+2R)=1/2R+3
所以答案為E

[applepeko]

哇 ! 懂了懂了...謝謝吶!!!