Question

A solar-panel company counted 69 invoices at the end of the month. They charge $400 for a new installation and $25 fora service call. The total dollar amount of the invoices was $6,975. How many service calls were made?

Answer 1

The number of service calls made = 55

Explanation:

Let the total number of installations made by the company = x

Let the total number of service calls = y

Total number of invoices for the month = 69

=>
`\[x+y=69\]` -------------------(1)

Total amount of the invoices = $6975

=>
`\[400x+25y=6975\]` -----------(2)

From (1),
`\[y=69-x\]`

Substituting in (2):

=>
`\[400x+25*(69-x)=6975\]`

=>
`\[400x+1725-25x=6975\]`

=>
`\[375x=5250\]`

=>
`\[x=14\]`

`\[y=69-x\]`

=>
`\[y=55\]`