John the car salesman makes a commission on selling cars, as a percentage of the price, which

depends on the car being new or used ("PreOwned"?). His commission on used cars is 50% more

than on new cars. In a particular month he sells new cars worth $80,000 and used cars worth

$50,000, and his commission check is $3,100.

(a) If x represents the commission percentage on new cars, express the commission percentage

on used cars in terms of x.

John's commission percentage on new cars is x and his commission percentage on used cars is 1.5x, therefore, John's commission percentage on new cars is 2% and his commission percentage on used cars is 3%.

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

John's commission percentage on new cars = x

John's commission percentage on used cars = x + 50%x (His commission on used cars is 50% more than on new cars)

Sales on new cars = $80,000

Sales on used cars = $50,000

John's commission check = $3,100

2. If x represents the commission percentage on new cars, express the commission percentage on used cars in terms of x.

John's commission percentage on new cars = x

John's commission percentage on used cars = x + 50%x = 1.5x

Now we can solve for x, this way:

80,000x + 50,000 * 1.5x = 3,100

80,000x + 75,000x = 3,100

155,000x = 3,100

x = 3,100/155,000

x = 0.02 = 2% ⇒ 1.5x = 3%

John's commission percentage on new cars is 2% and his commission percentage on used cars is 3%