Question

The total number of seats in a movie theater is calculated by adding the area of the upper section given by 8x2 and the area of the lower section given by 6x2. The theater plans to add an addition of front row seats given by 4x for a total of 138 seats. Which equation could be used to solve for the number of seats in the front row addition?

Answer 1

8x^2+6x^2+4x=138  combine like terms on left side

14x^2+4x=138 since the number of seats in the from row is just 4x, subtract 14x^2 from both sides

4x=138-14x^2  that would be the general solution, if you wanted the actual number you would have to solve for x and then multiply that value by 4 to know what "4x" is...

14x^2+4x-138=0

14x^2-42x+46x-138=0

14x(x-3)+46(x-3)=0

(14x+46)(x-3)=0

2(7x+23)(x-3)=0, since x>0

x=3 and thus

4x=12 seats

So there are 12 seats in the front row addition.