Algebra HELP SAT math question

Question

A theater can seat 744 people. The number of rows is 7 less than the number of seats in each row. How many rows of seats are there?

Answer 1

x*(x-7)=744

x^2-7x=744

x=23.628

Answer 2

Think of this problem as similar to an area problem. The seats are the length or columns of an array; the rows are the width or rows of an array. So the 744 seats are like the area. I like to use variable letters that represent the things. So the main equation is going to be:

S * R = 744

S = Seats

R = S - 7

The working equation then will be:

S (S-7) = 744

S² - 7S = 744

S²- 7S - 744 = 0

Factor the trinomial:

(S - 31) (S + 24) = 0

Set each factor as a separate relationship equation to find how many seats:

S - 31 = 0 and S + 24 = 0

S = 31 or S = -24

Since you can't have a negative number of seats, there must be 31 seats in each row.

When you go back to the original relationship, the rows will be S - 7,

which means the 24 will be how many rows.

The prompt asked for how many rows, so the answer to select will be 24.