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Emma began with 120000 dollars. She used part of this money to purchase a car. Of the remaining amount, she invested \frac{2}{5} at 3% simple annual interest and \frac{3}{5} at 5% simple annual interest. If after one year her total interest income was 2100 dollars, what was the purchase price of the car?

Explanation	Calculations	Help
$We name the purchase price variable and express the remaining amount to invest.$	$x = purchase price of the car 120000 - x = remaining amount to invest$
$We calculate the weighted simple interest rate on the remaining amount.$	$\frac{2}{5} \times 3% + \frac{3}{5} \times 5% = \frac{6}{5} % + 3% = \frac{6}{5} % + \frac{15}{5} % = \frac{21}{5} %$
$We translate the total interest income into an equation using the percent rate and the remaining amount.$	$(120000 - x) \times \frac{\frac{21}{5}}{100} = 2100$	Theory & Tactics Method Card FDPR4-A Click to view full details
$We solve for the remaining amount by isolating and simplifying the fraction.$	$120000 - x = 2100 \times \frac{100}{\frac{21}{5}} = 2100 \times \frac{500}{21}$
$We simplify the product by cancelling common factors.$	$2100 \times \frac{500}{21} = \frac{21 \times 100 \times 500}{21} = 100 \times 500 = 50000$	Theory & Tactics Method Card FDPR2-A Click to view full details
$We subtract the remaining amount from 120000 to find the purchase price.$	$120000 - x = 50000 x = 120000 - 50000 = 70000$

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B

Emma began with 120000 dollars. She used part of this money to purchase a car. Of the remaining amount, she invested \frac{2}{5} at 3% simple annual interest and \frac{3}{5} at 5% simple annual interest. If after one year her total interest income was 2100 dollars, what was the purchase price of the car?

Explanation	Calculations	Help
$We name the purchase price variable and express the remaining amount to invest.$	$x = purchase price of the car 120000 - x = remaining amount to invest$
$We calculate the weighted simple interest rate on the remaining amount.$	$\frac{2}{5} \times 3% + \frac{3}{5} \times 5% = \frac{6}{5} % + 3% = \frac{6}{5} % + \frac{15}{5} % = \frac{21}{5} %$
$We translate the total interest income into an equation using the percent rate and the remaining amount.$	$(120000 - x) \times \frac{\frac{21}{5}}{100} = 2100$	Theory & Tactics Method Card FDPR4-A Click to view full details
$We solve for the remaining amount by isolating and simplifying the fraction.$	$120000 - x = 2100 \times \frac{100}{\frac{21}{5}} = 2100 \times \frac{500}{21}$
$We simplify the product by cancelling common factors.$	$2100 \times \frac{500}{21} = \frac{21 \times 100 \times 500}{21} = 100 \times 500 = 50000$	Theory & Tactics Method Card FDPR2-A Click to view full details
$We subtract the remaining amount from 120000 to find the purchase price.$	$120000 - x = 50000 x = 120000 - 50000 = 70000$

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B