Question

A particular movie theater charges $ 9.00 per adult ticket and $ 3.5 0 per child ticket. Suppose 550 people attended a movie and the total revenue from ticket sales was $ 3575 . Write two linear equations to represent a system to solve this, where x represents the number of adults attending the movie and y represents the number of children attending the movie. Write the equations, but do not solve them. The first equation must come from the information given about the total attendance and the second must come from the ticket prices and revenue. 1)= ? 2)= ?

Answer 1

If x represents the no. of adults

and y represents the children, then

x + y = 550

9x + 3.50y = 3575

Answer 2

Explanation:

Number of children = y

Number of adults = x

Total people = 550

x + y = 550 ------------------ (I)

Charge for 'y' children =3.50 * y = 3.5y

Charge for 'x' adult = 9 * x = 9x

Total amount = $ 3575

9x + 3.5y = 3575 -------------(II)

Multiply equation (I) by (-9)

(I)*(-9) -9x - 9y = -4950

(II) 9x + 3.5y = 3575 { Now add and so 'x' will be eliminated}

- 5.5y = -1375

y = -1375/-5.5

y = 250

Plug in y = 250 in equation (I)

x + 250 = 550

x = 550 - 250

x = 300

Number of children = 250

Number of adults = 300