Sophia had saved $110{,}000$...... | Free GMAT Practice Question | GMAT Panda

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Sophia had saved 110, 000 dollars. She used part of these savings to purchase a car. Of the remaining amount, she invested \frac{2}{5} of it at 4 percent simple annual interest and \frac{3}{5} of it at 9 percent simple annual interest. If after one year the total interest from the two investments was 3, 500 dollars, what was the purchase price of the car?

Explanation	Calculations	Help
$We name the purchase price variable and express the remaining amount available for investment.$	$x = purchase price of the car 110000 - x = amount invested$
$We calculate the overall simple interest rate on the invested amount by weighting the two rates according to the given fractions.$	$\frac{2}{5} \times 4% + \frac{3}{5} \times 9% = \frac{8}{5} % + \frac{27}{5} % = \frac{35}{5} % = 7%$
$We translate the total annual interest into an equation using the simple interest rate and the invested amount.$	$(110000 - x) \times 7% = 3500$	Theory & Tactics Method Card FDPR4-A Click to view full details
$We isolate the invested amount by dividing the total interest by the interest rate.$	$110000 - x = 3500 \times \frac{100}{7}$
$We simplify the product by cancelling the factor of 7 in the numerator and denominator.$	$3500 \times \frac{100}{7} = \frac{7 \times 500 \times 100}{7} = 500 \times 100 = 50000$	Theory & Tactics Method Card FDPR2-A Click to view full details
$We subtract the invested amount from the total savings to find the purchase price of the car.$	$110000 - x = 50000 x = 110000 - 50000 = 60000$

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A

Sophia had saved 110, 000 dollars. She used part of these savings to purchase a car. Of the remaining amount, she invested \frac{2}{5} of it at 4 percent simple annual interest and \frac{3}{5} of it at 9 percent simple annual interest. If after one year the total interest from the two investments was 3, 500 dollars, what was the purchase price of the car?

Explanation	Calculations	Help
$We name the purchase price variable and express the remaining amount available for investment.$	$x = purchase price of the car 110000 - x = amount invested$
$We calculate the overall simple interest rate on the invested amount by weighting the two rates according to the given fractions.$	$\frac{2}{5} \times 4% + \frac{3}{5} \times 9% = \frac{8}{5} % + \frac{27}{5} % = \frac{35}{5} % = 7%$
$We translate the total annual interest into an equation using the simple interest rate and the invested amount.$	$(110000 - x) \times 7% = 3500$	Theory & Tactics Method Card FDPR4-A Click to view full details
$We isolate the invested amount by dividing the total interest by the interest rate.$	$110000 - x = 3500 \times \frac{100}{7}$
$We simplify the product by cancelling the factor of 7 in the numerator and denominator.$	$3500 \times \frac{100}{7} = \frac{7 \times 500 \times 100}{7} = 500 \times 100 = 50000$	Theory & Tactics Method Card FDPR2-A Click to view full details
$We subtract the invested amount from the total savings to find the purchase price of the car.$	$110000 - x = 50000 x = 110000 - 50000 = 60000$

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A