A theater can seat 638 people. The number of rows is 7 less than the number of seats in each row. How many rows of seats are there?

rows =x seats per row=x+7 and total seats = rows times seats per row or x(x+7) or x^2+7x=seats =638 so if you subtract 638 from both sides you can get an equation thatyou can factor out (x^2+7x-638)=0 638 factors out to 2 times 11 times 29 so (x-22)(x+29)=0 so x-22=0 x=22 or x+29=0 x=-29 but you can't have a negative number of rows so this answer is wrong so the answer is there are 22 rows and 29 seats (22+7=29)

Answered by apologiabiology | 2024-06-10

form an equation using the information given. x = number of sets in a row x - 7 = number of rows x(x - 7) = 638 x^2 - 7x = 638 make a quadratic equation x^2 - 7x - 638 = 0 then solve either using quadratic equation or find two numbers that add to make -7 and multiply to make -638, one number is negative and one is positive, as the product of the numbers is negative. -29 + 22 = -7 -29 x 22 = -639 then put into brackets (x - 29)(x + 22) = 0 when the equation equals zero you can find two values for x x = 29 or -22

Answered by RhysH | 2024-06-10

The theater has 22 rows of seats. Each row contains 29 seats, providing a total capacity of 638 seats. This was determined by solving the quadratic equation set up from the problem.
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Answered by apologiabiology | 2024-12-26