Question

Luisa earns money mowing her neighbors' lawns.

Answer 1

Answer:

$p(x)=16x-25$

C is the correct option.

Step-by-step 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.

Answer 2

Answer:

C. p(x) =  16x - 25

Step-by-step 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