Question

A roofing company counted 65 invoices at the end of the month. They charge $490 for a new installation and $68 for a repair. The total dollar amount of the invoices was $10,750. How many new roofs were installed?

Answer 1

By setting up a system of equations with the given information, we determine that the roofing company installed 15 new roofs.

Step-by-step explanation:

The student is asking to determine the number of new roofs installed by a roofing company given the total number of invoices, the charge for new installations and repairs, and the total dollar amount of the invoices. To find the answer, we need to set up a system of equations based on the given information:

1. Let x represent the number of new installations.
2. Let y represent the number of repairs.
3. The company counted 65 invoices: x + y = 65
4. The total amount for installations and repairs is $10,750: 490x + 68y = 10,750.

By solving this system of equations, we can find the value of x, which is the number of new installations.

First, we multiply both sides of the first equation by 68:

68x + 68y = 4,420

Now, we subtract this new equation from the second equation:

490x + 68y - (68x + 68y) = 10,750 - 4,420

422x = 6,330

Finally, we divide both sides by 422:

x = 15

Therefore, the roofing company installed 15 new roofs.

Answer 2

There were 15 installments of the roof.

Step-by-step explanation:

We are given the following information in the question:

Total number of invoice = 65

Cost of installation = $490

Cost of repair = $68

Total cost = $10,750

Let x be the number of installments and y be the number of repairs.

Then, we can write the following equations:

`x + y = 65\\490x + 68y = 10750`

Solving the two equations in two variables, we get:

`68x + 68y = 4420\\490x + 68y = 10750\\490x - 68x = 10750 - 4420\\422x = 6330\\x = 15\\\text{Putting value of x in one of the equation}\\15 + y = 65\\y =65-15 = 50`

Thus, there were 15 installments and 50 repairs of the roof.