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 1/3 of it at 4 percent simple annual interest and 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?

GMAT Panda · Accepted Answer

94,000USD We name the purchase price variable and express the remaining amount to invest. x = purchase price of the house 100000 - x = remaining amount to invest We calculate the weighted simple interest rate on the remaining amount. 1/3 4% + 2/3 6% = 4/3% + 4% = 16/3% We translate the total interest income into an equation using the percent rate and the remaining amount. (100000 - x) 16/3100 = 320 We solve for the remaining amount by isolating 100000 - x. 100000 - x = 320 10016/3 = 320 300/16 We simplify the product by cancelling common factors. 320 300/16 = 16 20 30016 = 20 300 = 6000 We subtract the remaining amount from 100000 to find the purchase price. 100000 - x = 6000 x = 100000 - 6000 = 94000

Explanation	Calculations	Help
$We name the purchase price variable and express the remaining amount to invest.$	$x = purchase price of the house 100000 - x = remaining amount to invest$
$We calculate the weighted simple interest rate on the remaining amount.$	$\frac{1}{3} \times 4% + \frac{2}{3} \times 6% = \frac{4}{3} % + 4% = \frac{16}{3} %$
$We translate the total interest income into an equation using the percent rate and the remaining amount.$	$(100000 - x) \times \frac{\frac{16}{3}}{100} = 320$
$We solve for the remaining amount by isolating 100000 - x .$	$100000 - x = 320 \times \frac{100}{\frac{16}{3}} = 320 \times \frac{300}{16}$
$We simplify the product by cancelling common factors.$	$320 \times \frac{300}{16} = \frac{16 \times 20 \times 300}{16} = 20 \times 300 = 6000$
$We subtract the remaining amount from 100000 to find the purchase price.$	$100000 - x = 6000 x = 100000 - 6000 = 94000$

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