20. the commission earned on the sale of a car can be represented by the equation c(p)=250 + 0.02p where c…

20. the commission earned on the sale of a car can be represented by the equation c(p)=250 + 0.02p where c represents the commission and p represents the purchase price of the car. a) jack sold two cars last weekend, one for $15,075 and the other for $21,640. find his total commission. b) if c(p)=745.80, find the purchase price of the car.

20. the commission earned on the sale of a car can be represented by the equation c(p)=250 + 0.02p where c represents the commission and p represents the purchase price of the car. a) jack sold two cars last weekend, one for $15,075 and the other for $21,640. find his total commission. b) if c(p)=745.80, find the purchase price of the car.

Answer

Explanation:

Step1: Calculate commission for first car

Substitute $p = 15075$ into $c(p)=250 + 0.02p$. $c_1=250+0.02\times15075=250 + 301.5=551.5$

Step2: Calculate commission for second car

Substitute $p = 21640$ into $c(p)=250 + 0.02p$. $c_2=250+0.02\times21640=250 + 432.8 = 682.8$

Step3: Calculate total commission for part a

Add the two commissions together. $c_{total}=c_1 + c_2=551.5+682.8 = 1234.3$

Step4: Solve for $p$ in part b

Set $c(p)=745.80$, so $745.80=250 + 0.02p$. First, subtract 250 from both sides: $745.80 - 250=0.02p$. $495.80 = 0.02p$. Then, divide both sides by 0.02 to solve for $p$. $p=\frac{495.80}{0.02}=24790$

Answer:

a) $1234.3$ b) $24790$