GMAT Practice Question: 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?
- 2,400USD
- 2,464USD
- 2,650USD
- 2,732USD
- 2,800USD
Topics: word problems, profit/loss, percentages, linear equations, translations
Solution
Step 1
We first name an unknown to represent the store's cost for the computer.
C = \text{store's cost for the computer}
Step 2
We translate \textbf{"selling price of 2,240USD"} minus the cost equals \textbf{"profit of 40 percent of the store's cost"}.
2240 - C = \frac{40}{100} \times C
Step 3
We isolate the cost by combining like terms.
2240 = \frac{140}{100} \times C
Step 4
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}
Step 5
We simplify the fractions by cancelling out terms
C = \frac{\cancel{140} \times 15 \times 100}{\cancel{140}} + \frac{\cancel{140} \times 100}{\cancel{140}} = 1500 + 100 = 1600
Step 6
We translate \textbf{"profit of 50 percent of the computer's cost"} into the new selling price formula.
\text{New SP} = C + \frac{50}{100} \times C = 1.5 \times C
Step 7
We substitute the cost into the formula to find the new selling price.
\text{New SP} = 1.5 \times 1600 = 2400
Answer
2400USD
