Question

he cost​ C, in​ dollars, of renting a moving truck for a day is given by the function Upper C left parenthesis x right parenthesis equals 0.25 x plus 40 comma where x is the number of miles driven.
​(a) What is the cost if a person drives x equals 240 ​miles?
​(b) If the cost of renting the moving truck is ​$180​, how many miles did the person​ drive?
​(c) Suppose that a person wants the cost to be no more than ​$150. What is the maximum number of miles the person can​ drive?

Answer 1

Answer:

C = 0.25x + 40

(a) For this part we solve for C when x = 240. Substitute 240 in for x.

C = 0.25(240) + 40

Multiply 240 by 0.25.

C = 60 + 40

Add.

C = 100

The cost is $100.

Check

100 = 0.25(240) + 40

100 = 60 + 40

100 = 100

(b) For this part we solve for x when C = 180. Substitute 180 for C.

180 = 0.25x + 40

Subtract 40 from each side.

140 = 0.25x

Divide each side by 0.25.

560 = x

This person drove 560 miles.

Check

180 = 0.25(560) + 40

180 = 140 + 40

180 = 180

(c) For this we must make an inequality with C = 150.

Since they want the cost to be no more than 150, we will use the ≥ symbol.

C ≥ 0.25x + 40

Substitute 150 for C. Solve for x.

150 ≥ 0.25x + 40

Subtract 40 from each side.

110 ≥ 0.25x

Divide each side by 0.25.

440 ≥ x

The maximum number of miles they can drive is 440.

Check

150 ≥ 0.25(440) + 40

150 ≥ 110 + 40

150 ≥ 150