Question

certified remodeling advertises their business prices by the function $c(x)=25x + 50$, which represents the labor cost (in dollars), where $x$ is the number of hours of labor.

which company would be better if the deck were to take 8 hours?

$circ$ certified remodeling
$circ$ master remodeling

master remodeling advertises their business with the table shown below...

hours	cost
4	$160
6	$190

Explanation:

Step1: Find cost for Certified Remodeling at 8 hours

Use the function \( c(x) = 25x + 50 \). Substitute \( x = 8 \):
\( c(8) = 25(8) + 50 = 200 + 50 = 250 \) dollars.

Step2: Find the cost function for Master Remodeling

First, find the slope \( m \) using two points, e.g., (2, 130) and (4, 160):
\( m = \frac{160 - 130}{4 - 2} = \frac{30}{2} = 15 \).
Using point - slope form \( y - y_1 = m(x - x_1) \) with (2, 130):
\( y - 130 = 15(x - 2) \)
\( y = 15x - 30 + 130 = 15x + 100 \).

Step3: Find cost for Master Remodeling at 8 hours

Substitute \( x = 8 \) into \( y = 15x + 100 \):
\( y = 15(8) + 100 = 120 + 100 = 220 \) dollars.

Step4: Compare the two costs

Certified Remodeling costs 250 dollars, Master Remodeling costs 220 dollars. Since 220 < 250, Master Remodeling is cheaper.

Answer:

Master Remodeling