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?
The car would have to sell for $
for both job opportunities to pay Jim the same amount.

Answer 1

The car would have to sell for $ 487.804 for both job opportunities to pay Jim the same amount.

Solution:

Let car's price be x

Ace Cars says they will pay Jim a 10% commission on the sale price of each car

Therefore,

Jim payment = x + 10 % of x

`Jim\ payment = x + (10)/(100) * x\\\\Jim\ payment = x + 0.1x = 1.1x`

Budget Cars says they will pay him $500 per week plus a 7.5% commission on the sale price of each car

Jim payment = 500 + 7.5 % of x

`Jim\ payment = 500 + (7.5)/(100)x\\\\Jim\ payment = 500 + 0.075x`

What price would the car have to sell for in order for these two job opportunities to pay Jim the same amount

Therefore,

Both the payment should be equated

1.1x = 500 + 0.075x

1.1x - 0.075x = 500

1.025x = 500

x = 487.804

The car would have to sell for $ 487.804 for both job opportunities to pay Jim the same amount.