A store's selling price of 2,240USD for a certain computer would yield a profit of 40 percent of...

Question

A store's selling price of 2,240USD for a certain computer would yield a profit of 40 percent of the store's cost for the computer. What selling price would yield a profit of 50 percent of the computer's cost?

GMAT Panda · Accepted Answer

2400USD We first name an unknown to represent the store's cost for the computer. C = store's cost for the computer We translate "selling price of 2,240USD" minus the cost equals "profit of 40 percent of the store's cost". 2240 - C = 40/100 C We isolate the cost by combining like terms. 2240 = 140/100 C We solve for the store's cost by dividing both sides by 140 and multiplying by 100. C = 2240 100/140 = 2100 100/140 + 140 100/140 We simplify the fractions by cancelling out terms C = 140 15 100140 + 140 100140 = 1500 + 100 = 1600 We translate "profit of 50 percent of the computer's cost" into the new selling price formula. New SP = C + 50/100 C = 1.5 C We substitute the cost into the formula to find the new selling price. New SP = 1.5 1600 = 2400

Explanation	Calculations	Help
$We first name an unknown to represent the store's cost for the computer.$	$C = store’s cost for the computer$
$We translate "selling price of 2,240USD" minus the cost equals "profit of 40 percent of the store's cost" .$	$2240 - C = \frac{40}{100} \times C$
$We isolate the cost by combining like terms.$	$2240 = \frac{140}{100} \times C$
$We solve for the store's cost by dividing both sides by 140 and multiplying by 100.$	$C = \frac{2240 \times 100}{140} = \frac{2100 \times 100}{140} + \frac{140 \times 100}{140}$
$We simplify the fractions by cancelling out terms$	$C = \frac{140 \times 15 \times 100}{140} + \frac{140 \times 100}{140} = 1500 + 100 = 1600$
$We translate "profit of 50 percent of the computer's cost" into the new selling price formula.$	$New SP = C + \frac{50}{100} \times C = 1.5 \times C$
$We substitute the cost into the formula to find the new selling price.$	$New SP = 1.5 \times 1600 = 2400$

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