please help

[anjaligeorge1]

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

[pinktiger]

Good Question. Even I got this one wrong.

This is I found posted by somebody else -

let his income this year = $i

and he saves $x this year

spending this year = i-x

next year:

for each dollar he saves this year he will have available $(1+r) to spend

total amount available for him to spend next year = x(1+r)

which will be equal to half the spending this year

so, x(1+r) = (i-x)/2

=> x/i = 1/(2r+3)