Bunuel wrote:
Bob, Peter, and Stan are going to combine all their savings to invest in a business. The amount of money in Bob’s savings is 2/3 of the amount in Stan’s savings. The amount in Peter’s savings is double the amount in Stan’s savings. If Stan decides to invest only 3/4 of his savings into the business, then the amount that Stan invests will be what fraction of the amount that Bob and Peter invest combined?
A 1/8
B 9/44
C 1/4
D 9/32
E 3/8
Stated as B=Bob's savings; P=Peter's savings; S=Stan's savings.
Thus as stated in the stem of the question: \(B=\frac{2}{3}S\) and \(P=2S\).
Stan invests \(\frac{3}{4}\) of his savings thus \(\frac{3}{4}S\).
The amount that Bob and Peter invest together is \(\frac{2}{3}S+2S=\frac{8}{3}S\).
The fraction is \(\frac{3}{4}*\frac{3}{8}\) is equal to \(\frac{9}{32}\).
Answer D