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 $85.00​ for 8 feet of pipe and a second customer pays $145.00​ for 20​ feet of pipe. How many feet of pipe did a customer need if they paid $295.00​?

Answer 1

To solve this problem, set up a system of equations using the given information. Solve the system to find the values of the service fee and cost per foot of pipe. Use these values to determine the number of feet of pipe needed if a customer paid $295.00. Therefore, the customer needed 50 feet of pipe if they paid $295.00.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's call the service fee F and the cost per foot of pipe C. We can write two equations based on the information given:

For the first customer: F + 8C = 85.00

For the second customer: F + 20C = 145.00

Now, we can solve this system of equations to find the values of F and C. Subtracting the first equation from the second equation, we get:

12C = 60.00

Dividing both sides by 12, we find that C = 5.00. Plugging this value back into the first equation, we can solve for F:

F + 8(5.00) = 85.00

F + 40 = 85.00

F = 45.00

Now that we have the values of F and C, we can use them to find the number of feet of pipe needed if a customer paid $295.00:

45.00 + NC = 295.00

Subtracting 45.00 from both sides, we have:

NC = 250.00

Dividing both sides by 5.00, we get:

N = 50.00

Therefore, the customer needed 50 feet of pipe if they paid $295.00.

Answer 2

The customer needed 50 feet of pipe if they paid $295.00.

The first customer paid $85.00 for 8 feet of pipe, so the equation is S + 8P = 85.

The second customer paid $145.00 for 20 feet of pipe, so the equation is S + 20P = 145.

Solving these equations:

Subtracting the first equation from the second:

20P - 8P = 145 - 85

12P = 60

P = 5

Now that we have P = 5, substitute it back into the first equation:

S + 8(5) = 85

S + 40 = 85

S = 45

So, the service fee (S) is $45.00, and the price per foot of pipe (P) is $5.00.

Now, use these values to find how many feet of pipe a customer needed if they paid $295.00:

45 + 5x = 295

Subtract 45 from both sides:

5x = 250

Divide by 5:

x = 50

Therefore, the customer needed 50 feet of pipe if they paid $295.00.