Question

Ace Cars says they will pay Jim a 10% commission on the sale price of each car. Budget Cars says they will pay him $500 per week plus a 7.5% commission on the sale price of each car. Jim can sell one car every week. What price would the car have to sell for in order for these two job opportunities to pay Jim the same amount?

Answer 1

$20,000

Explanation:

You can quickly figure this by recognizing that the difference in commission must be the same as the base salary:

2.5%(car price) = $500

car price = $500/0.025 = $20,000

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If you prefer, you can get there with equations.

At Job 1, the pay is ...

y = 10%×(car price)

At Job 2, the pay is ...

y = 7.5%×(car price)

Setting the equal (the two opportunities pay the same), we have ...

0.10(car price) = 500 +0.075(car price)

0.025(car price) = 500 . . . . . . . . subtract 0.075(car price)

car price = 500/0.025 = 20,000 . . . . divide by 0.025

Jim would have to sell a $20,000 car each week for the jobs to pay the same.