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?

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, .....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 = $ = $

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 = $ = $

The total receipts for the week = $4189.77

So we can write the equation as,

.....equation 2

From equation 1, we can write,

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

By distributing 189.99 we will get,

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

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

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

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

The number of four door sedans = .

We have got the required answer here.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap