Question

a plumber charges a flat fee of $74 to visit a home and examine a clogged drain. the plumber charges an additional $28 per hour spent fixing the drain. the total cost, c (in dollars), for fixing a drain that takes h hours is given by the following function.
c(h) = 28h + 74
answer the following questions.
(a) what is the total cost for fixing a drain that takes 6 hours?
$
(b) if the plumber charged a total of $382, how many hours did she spend fixing the drain?
hours

Explanation:

Part (a)

Step1: Identify the function and input

The cost function is \( C(h) = 28h + 74 \), and we need to find \( C(6) \) (since \( h = 6 \) hours).

Step2: Substitute \( h = 6 \) into the function

Substitute \( h = 6 \) into \( C(h) \):
\( C(6) = 28(6) + 74 \)
First, calculate \( 28 \times 6 = 168 \).
Then, add 74: \( 168 + 74 = 242 \).

Step1: Set up the equation

We know \( C(h) = 382 \), so substitute into \( C(h) = 28h + 74 \):
\( 382 = 28h + 74 \)

Step2: Solve for \( h \)

Subtract 74 from both sides:
\( 382 - 74 = 28h \)
\( 308 = 28h \)
Divide both sides by 28:
\( h = \frac{308}{28} = 11 \)

Answer:

(a):
\( \$242 \)

Part (b)