Question

Nick Chapp manages an Auto Film outlet that applies window film to automobile windows. He reported that this past week, a total of 23 autos had window film applied. Auto Film charges $189.99 for a four-door sedan and $159.99 for a two-door coupe. If Nick had total receipts for the week of $4189.77, how many four-door sedans had been serviced? How many two-door coupes?

Answer 1

Let, the number of four door sedans = x

And the number of two door coupes = y

Given a total of 23 autos had window film applied.

So we can write the equation as,
`x+y = 23` .....equation 1

The charge of auto film for a four door sedan = $189.99.

Now the charge of auto film for x four door sedans = $
`(189.99)(x)` = $
`(189.99x)`

Also given, the charge of auto film for a two door coupe = $159.99.

So, the charge of auto film for y two doos coupes = $
`(159.99)(y)` = $
`(159.99y)`

The total receipts for the week = $4189.77

So we can write the equation as,

`189.99x + 159.99y = 4189.77` .....equation 2

From equation 1, we can write,
`x = 23-y`

Now by substituting this value of x in equation 2 we will get,

`189.99 (23-y) + 159.99y = 4189.77`

By distributing 189.99 we will get,

`4369.77 - 189.99y +159.99y = 4189.77`

`4369.77-30y = 4189.77`

To get y first we move 30y to the right side by adding it to both sides. We will get,

`4369.77-30y+30y = 4189.77 +30y`

`4369.77 = 4189.77+30y`

Now to get y , we will move 4189.77 to the left side by subtracting it from both sides. We will get,

`4369.77-4189.77 = 4189.77-4189.77+30y`

`180 = 30y`

Now to get , we will move 30 to the left side by dividing it to both sides. We will get,

`(180)/(30) =(30y)/(30)`

`(180)/(30) = y`

`6 = y`

`y = 6`

So we have got the number of two door coupes = 6

The number of four door sedans =
`(23-6) = 17`.

We have got the required answer here.