GWD27-Q19

nicboy

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)

有人说是 S(1+r)= 0.5(T-S), S--saving, T- Income, 但好像这样也求不出来，能手指教

zuodun

题目问得what fraction of his income ， 就是求他收入的几分之几，根据你列的式子得到s=1/（2r+3）T ，答案自然就是E了

bth

Let x = amount saved
y = amount spent
Total income = x + y
The question asked to determine x/(x+y) in terms of r.

 

Accordingly,
x(1+r) = y/2
y = 2x(1+r)
Therefore x/(x+y) = fraction of total income

= x/(x + (2x(1+r)))

=x/(x+2x+2xr)

=x/[x(1+2+2r)]

=1/(3+2r)

 

Answer is E