Question

Luisa earns money mowing her neighbors' lawns.

The revenue for mowing x lawns is r(x) = 20x.
Luisa's cost for gas and the mower rental is c(x) = 4x + 25.

Her profit from mowing x lawns is p(x) = (r – c)(x). What is p(x)?

A. p(x) = 24x – 25

B. p(x) = 16x + 25

C. p(x) = 16x – 25

D. p(x) = 24x + 25

Answer 1

C. p(x) = 16x - 25

Explanation:

1. First define the equation that describes the profit Luisa earns, that is the revenue for mowing minus the Luisa´s cost for gas and the mower rental. So the equation is:

p(x) = (r – c)(x) (Eq.1)

2. Write the equations for the revenue for mowing and the cost for gas and the mower rental:

- Equation for the revenue for mowing:

r(x) = 20x (Eq.2)

- Equation for the cost for gas and the mower rental:

c(x) = 4x + 25 (Eq.3)

3. Replace the equations Eq. 2 and Eq. 3 in Eq. 1:

p(x) = (r – c)(x)

p(x) = 20x - (4x + 25)

p(x) = 20x - 4x - 25

p(x) = 16x - 25

Answer 2

`p(x)=16x-25`

C is the correct option.

Explanation:

We have been given that

`r(x)=20x\\c(x)=4x+25`

The profit is the difference of revenue and cost function.

Mathematically, we can write profit function as

`p(x)=(r-c)x`

We know that
`(f-g)(x)=f(x)-g(x)`. Thus, we have

`p(x)=r(x)-c(x)`

Plugging, the r(x) and c(x) functions

`p(x)=20x-(4x+25)`

Distribute negative over the parenthesis

`p(x)=20x-4x-25`

Combine the like terms. 20x-4x = 16x

`p(x)=16x-25`

C is the correct option.