BTGmoderatorLU wrote: ↑

Wed Jan 27, 2021 11:35 am

Source: Manhattan Prep

At the beginning of 2011, Albert invests $15,000 at 10% simple annual interest, $6,000 at 7% simple annual interest, and $x at 8% simple annual interest. If, by the end of 2011, Albert receives interest totaling 9% of the sum of his three investments, then the ratio of $x to the sum of his two other investments is

A. 1:3
B. 1:4
C. 1:6
D. 1:7
E. 1:8

The OA is D

Solution:

Using the formula Interest = Rate x Time, we can create the equation for the total interest earned by the 3 investments, letting x equal the amount invested at 8% simple interest:

15,000 * 0.1 + 6,000 * 0.07 + x * 0.08 = (15,000 + 6,000 + x) * 0.09

1,500 + 420 + 0.08x = 1,890 + 0.09x

30 = 0.01x

3,000 = x

Therefore, the desired ratio is 3,000 : (15,000 + 6,000) = 3,000 : 21,000 = 1:7.

Answer: D