Problem Solving

adthedaddy wrote: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)

Mitch's input-output approach is the best (fastest) approach, but here's an algebraic solution as well:



Answer = E

Cheers,
Brent

By the way, this question is known as a "Variables in the Answer Choices" question.
The good thing about these questions is that there are typically 2 approaches you can take:
1) Algebraic
2) Input-Output

I recently wrote 2 articles on this topic:
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Cheers,
Brent

Abhijit K wrote: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)

We can let s = the amount of money, in dollars, Henry saves this year and t = his income, in dollars, this year; thus, the amount that he spends this year is (t - s). Since for each dollar that he saves this year he has 1 + r dollars available to spend next year, he has s(1 + r) dollars to spend next year. Furthermore, since this amount is half what he spends this year, we have:

s(1 + r) = (1/2)(t - s)

2s(1 + r) = t - s

2s + 2sr = t - s

2sr + 3s = t

s(2r + 3) = t

s = t/(2r + 3)

s = [1/(2r + 3)] * t

So, the amount he saves this year is 1/(2r + 3) of his income.

Answer: E