Flooring City is running a limited time special on carpeting. The cost to have your home carpeted is $100 per room and a $50 flat fee for installation.

Question

Part III: Using your equation from Part I, determine how much it would cost to have 4 rooms carpeted by Flooring City. Show ALL your work.

Part 1: The variables below are defined. Write a linear equation in slope-intercept form to represent the cost to have floors carpeted. The cost per room is $100 since r is the number of rooms. And the installation fee is $50. Now we have to find c, which is the total cost. The equation I will be using is slope intercept form, where mx is 100r and b is 50. c = 100r + 50.

Answer 1

To find the total cost of carpeting, we started with the equation you derived:

\[ c = 100r + 50 \]

where:

• \( c \) represents the total cost,
• \( r \) is the number of rooms,
• \( 100 \) is the cost per room, and
• \( 50 \) is the flat installation fee.

Now, to determine the cost for 4 rooms (\( r = 4 \)), we substitute \( 4 \) for \( r \) in the equation:

\[ c = 100(4) + 50 \]

Now we calculate it step-by-step:

1. Multiply \( 100 \) by \( 4 \):

\[ 100 \times 4 = 400 \]

2. Add the installation fee of \( 50 \):

\[ 400 + 50 = 450 \]

So, the total cost to have 4 rooms carpeted by Flooring City would be:

\[ c = 450 \]

Thus, the total cost for carpeting 4 rooms is $450.