Question

A plumber will reroute pipes at your home. the company charges the customer a service fee plus the price for each foot of pipe needed to finish the job. a customer pays $90.00 for 10 feet of pipe and a second customer pays $144.00 for 19 feet of pipe. how many feet of pipe did a customer need if they paid $312.00?

Answer 1

By setting up two equations based on the given costs and solving for the fixed service fee and cost per foot, we determine that a customer who paid $312.00 needed 47 feet of pipe.

Step-by-step explanation:

To solve the problem involving the plumber's charges, we need to find the cost per foot for the piping and the fixed service fee. After finding these amounts, we can calculate how many feet of pipe a customer needed when they paid $312.00.

Step-by-step Solution:

1. Let x represent the fixed service fee, and let y represent the cost per foot for the pipe.
2. We have two equations based on the information given: x + 10y = $90 and x + 19y = $144.
3. By solving the system of equations, we find the values for x and y.
4. Substitute the values of x and y into the equation x + ny = $312, where n is the number of feet of pipe, to find n.

Based on the equations:

• x + 10y = $90 (1)
• x + 19y = $144 (2)

By subtracting equation (1) from equation (2), we get:

• 9y = $54
• y = $54 ÷ 9
• y = $6 per foot

Substituting y in equation (1):

• x + 10 * $6 = $90
• x + $60 = $90
• x = $90 - $60
• x = $30 (service fee)

Now to find the number of feet (n) when the total cost is $312:

• 30 + 6n = $312
• 6n = $312 - $30
• 6n = $282
• n = $282 ÷ 6
• n = 47 feet

Therefore, a customer who paid $312.00 needed 47 feet of pipe.