Respuesta :
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, [tex] x+y = 23 [/tex] .....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 = $[tex] (189.99)(x) [/tex] = $[tex] (189.99x) [/tex]
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 = $[tex] (159.99)(y) [/tex] = $[tex] (159.99y) [/tex]
The total receipts for the week = $4189.77
So we can write the equation as,
[tex] 189.99x + 159.99y = 4189.77 [/tex] .....equation 2
From equation 1, we can write, [tex] x = 23-y [/tex]
Now by substituting this value of x in equation 2 we will get,
[tex] 189.99 (23-y) + 159.99y = 4189.77 [/tex]
By distributing 189.99 we will get,
[tex] 4369.77 - 189.99y +159.99y = 4189.77 [/tex]
[tex] 4369.77-30y = 4189.77 [/tex]
To get y first we move 30y to the right side by adding it to both sides. We will get,
[tex] 4369.77-30y+30y = 4189.77 +30y [/tex]
[tex] 4369.77 = 4189.77+30y [/tex]
Now to get y , we will move 4189.77 to the left side by subtracting it from both sides. We will get,
[tex] 4369.77-4189.77 = 4189.77-4189.77+30y [/tex]
[tex] 180 = 30y [/tex]
Now to get , we will move 30 to the left side by dividing it to both sides. We will get,
[tex] \frac{180}{30} =\frac{30y}{30}[/tex]
[tex] \frac{180}{30} = y [/tex]
[tex] 6 = y [/tex]
[tex] y = 6 [/tex]
So we have got the number of two door coupes = 6
The number of four door sedans = [tex] (23-6) = 17 [/tex].
We have got the required answer here.
