GMAT Practice Question: A company sells radios for 15.00 dollars each. It costs the company 14.00 dollars per radio to...
Question
A company sells radios for 15.00 dollars each. It costs the company 14.00 dollars per radio to produce 1,000 radios and 13.50 dollars per radio to produce 2,000 radios. How much greater will the company's gross profit be from the production and sale of 2,000 radios than from the production and sale of 1,000 radios?
- 500 dollars
- 1,000 dollars
- 1,500 dollars
- 2,000 dollars
- 2,500 dollars
Topics: word problems, profit/loss, revenue/cost, calculations, translations
Solution
Step 1
We first create variables for revenue, cost, and profit for 1,000 and 2,000 radios
R_{1000}, C_{1000}, P_{1000}, R_{2000}, C_{2000}, P_{2000}
Step 2
We translate \textbf{\text{"A company sells radios for 15.00 dollars each"}} and \textbf{\text{"production and sale of 1,000 radios"}} using the revenue formula
R_{1000}=15.00\times1000=15000
Step 3
We translate \textbf{\text{"costs the company 14.00 dollars per radio to produce 1,000 radios"}} using the cost formula
C_{1000}=14.00\times1000=14000
Step 4
We use the profit formula to find profit for 1,000 radios
P_{1000}=R_{1000}-C_{1000}=15000-14000=1000
Step 5
We translate \textbf{\text{"A company sells radios for 15.00 dollars each"}} and \textbf{\text{"production and sale of 2,000 radios"}} using the revenue formula
R_{2000}=15.00\times2000=30000
Step 6
We translate \textbf{\text{"13.50 dollars per radio to produce 2,000 radios"}} using the cost formula
C_{2000}=13.50\times2000=27000
Step 7
We use the profit formula to find profit for 2,000 radios
P_{2000}=R_{2000}-C_{2000}=30000-27000=3000
Step 8
We translate \textbf{\text{"How much greater will the company's gross profit be from the production and sale of 2,000 radios than from the production and sale of 1,000 radios?"}} using subtraction
\Delta P=P_{2000}-P_{1000}=3000-1000=2000
Answer
2000
