Final answer:
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:
- Let x represent the number of new installations.
- Let y represent the number of repairs.
- The company counted 65 invoices: x + y = 65
- 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.