GMAT Practice Question: A rug manufacturer produces rugs at a cost of 75USD per rug. What is the manufacturer's gross...
Question
A rug manufacturer produces rugs at a cost of 75USD per rug. What is the manufacturer's gross profit from the sale of 150 rugs if \frac{2}{3} of the rugs are sold for 150USD per rug and the rest are sold for 200USD per rug?
- 10,350USD
- 11,250USD
- 13,750USD
- 16,250USD
- 17,800USD
Topics: word problems, profit/loss, translations
Solution
Step 1
We define variables to represent each quantity:
R, N_{150}, N_{200}, Revenue, Cost, Profit
Step 2
We translate \textbf{\text{"2/3 of the rugs are sold for 150USD per rug"}} to find the number sold at 150USD.
N_{150} = \frac{2}{3} R = \frac{2}{3} \times 150 = 100
Step 3
We find the number sold at 200USD by subtracting the number sold at 150USD from the total.
N_{200} = R - N_{150} = 150 - 100 = 50
Step 4
We translate \textbf{\text{"sold for 150USD per rug"}} and \textbf{\text{"sold for 200USD per rug"}} into revenue expressions and sum them using the revenue formula.
Revenue = 150 \times N_{150} + 200 \times N_{200} = 150 \times 100 + 200 \times 50 = 15000 + 10000 = 25000
Step 5
We translate \textbf{\text{"produces rugs at a cost of 75USD per rug"}} into a cost expression using the cost formula.
Cost = 75 \times R = 75 \times 150 = 11250
Step 6
We calculate gross profit by applying \text{Profit} = \text{Revenue} - \text{Cost}.
Profit = Revenue - Cost = 25000 - 11250 = 13750
Answer
13,750 USD (Option C)
