GMAT Practice Question: David used part of 100,000USD to purchase a house. Of the remaining portion, he invested...
Question
David used part of 100,000USD to purchase a house. Of the remaining portion, he invested \frac{1}{3} of it at 4 percent simple annual interest and \frac{2}{3} of it at 6 percent simple annual interest. If after a year the income from the two investments totaled 320USD, what was the purchase price of the house?
- 96,000USD
- 94,000USD
- 88,000USD
- 75,000USD
- 40,000USD
Topics: word problems, percentages, interests - simple
Solution
Step 1
We name the purchase price variable and express the remaining amount to invest.
x = \text{purchase price of the house} 100000 - x = \text{remaining amount to invest}
Step 2
We calculate the weighted simple interest rate on the remaining amount.
\frac{1}{3} \times 4\% + \frac{2}{3} \times 6\% = \frac{4}{3}\% + 4\% = \frac{16}{3}\%
Step 3
We translate the total interest income into an equation using the percent rate and the remaining amount.
(100000 - x) \times \frac{\frac{16}{3}}{100} = 320
Step 4
We solve for the remaining amount by isolating 100000 - x.
100000 - x = 320 \times \frac{100}{\frac{16}{3}} = 320 \times \frac{300}{16}
Step 5
We simplify the product by cancelling common factors.
320 \times \frac{300}{16} = \frac{\cancel{16} \times 20 \times 300}{\cancel{16}} = 20 \times 300 = 6000
Step 6
We subtract the remaining amount from 100000 to find the purchase price.
100000 - x = 6000 x = 100000 - 6000 = 94000
Answer
94,000USD
