state the positive value(s) of x for which the production costs at the two sites are equal. explain how you determined your answer

Question

A company is considering a manufacturing plant. They determine the weekly production cost at site A to be A(x)=3x2 while the production cost at site B is B(x)=8x+3, where x represents the number of products, in hundreds, and A(x) and B(x) are the production costs, in hundreds of dollars.

Answer 1

A(x)=3x^2

B(x)=8x+3

A(x)=B(x)

3x^2=8x+3

3x^2-8x-3=0

factor

(3x+1)(x-3)=0

x-3=0

x=3

3(3^2)=8(3)+3

3(9)=24+3

27=27