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?
(A) 1 / (r+2)
(B) 1 / (2r+2)
(C) 1 / (3r+2)
(D) 1 / (r+3)
(E) 1 / (2r+3)
Let r=2.
Plug in values that satisfy the given conditions.
For each dollar that Henry saves this year, he will have 1+r = 1+2 = 3 dollars available to spend [next year]:
If he saves $1 this year, he can spend $3 next year.
Next year the amount he has available to spend will be equal to half the amount that he spends this year:
Since he has $3 to spend next year, he has $6 to spend this year.
What fraction of his income should Henry save this year?
Since he saves $1 and spends $6, saved/total = 1/(1+6) = 1/7. This is our target.
Now we plug r=2 into the answers to see which yields our target of 1/7.
Only
E works:
1/(2r+3) = 1/(2*2 + 3) = 1/7.
The correct answer is
E.
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