关于GWD中的一道数学题，有点郁闷！

akatsuki09

This year Henry will save a certain amountof his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he savesthis year, he will have 1 + r dollars available to spend.  In terms of r
, what fraction of hisincome should Henry save this year so that next year the amount he wasavailable 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)

Can anybody help me to figure it out?Thank you

Irenecy

Let's say the amount he has saved this year is X, and the amount he will have spent by the end of this year is Y.
Then he will have X(1+r) to spend next year.
So X(1+r)=Y/2, that is, Y=2X+2Xr
the fraction of the income saved is X/(X+Y)=X/(X+2X+2Xr)=1/(3+2r)

zhangfei3322

是这样啊

akatsuki09

Could you tell me some more about this kind of problem

akatsuki09

Oh mate.could u please further explain the process "Then he will have X(1+r) to spend next year.
So X(1+r)=Y/2",especially "X(1+r)"