Question

The first equation in the following system gives a company's income, in dollars, for selling x baseball caps. The second equation gives the cost of making x baseball caps. Y = 8x y = -0. 01 x2 4x 3,200 The solution of the system is (400, 3,200). How would you interpret this solution?.

Answer 1

The solution of the equation can be determined by substituting the points in the equation and solving it.

The solution of the given equation would be interpreted by solving the equation for the value of x and y.

The solution of the equation is (400, 3200) and it can be determined by using substitution method.

Given that,

The first equation in the following system gives a company's income, in dollars, for selling x baseball caps.

The second equation gives the cost of making x baseball caps.

$\rm y = 8x\\\\ y = -0.01 x^2 + 4x + 3200$

The solution of the system is (400, 3,200).

We have to determine,

How would you interpret this solution?

According to the question,

The first equation in the following system gives a company's income, in dollars, for selling x baseball caps.

The second equation gives the cost of making x baseball caps.

$\rm y = 8x\\\\ y = -0.01 x^2 + 4x + 3200$

On solving both the equation,

Substitute y = 8x in the equation 2,

$\rm y = -0.01 x^2 + 4x + 3200\\\\ 8x = -0.01 x^2 + 4x + 3200\\\\0.01x^2+8x-4x-3200=0\\\\0.01x (x+800) -4(x+800)=0\\\\(x+800)\ (0.01x-4)\\\\When \ \ x +800=0, \ x = -800\\\\And\ \ 0.01x-4 = 0, \ \ x = \dfrac{4}{0.01} \ \ x =400$

The value of x is not -800 because the cost can not be negative.

Then the value of x is 400.

Substitute the value of x in equation 1,

$\rm y = 8x\\\\y = 8(400)\\\\y = 3200$

Hence, The solution of the equation is (400, 3200).

For more details about System of Equation refer to the link given below.

https://brainly.com/question/281027