For matinees,a movie theater charges $7 per adult and $4 per child.if 84 people attended a matinee and paid a total of $432,How many adults and how many children were there .

First choose to let x=number of adults and y = number of children.

Then you can write 2 equations from the information given.

1) 7x + 4y = 432

2) X + y = 84

2) X + y = 84

Solve equation 2 for x: X = 84 – y

Substitute this value into equation 1:

7(84-y) + 4y = 432

588-7y + 4y =432

-3y = 432-588 = - 156

Y = -156/-3 = 52

So x= 84-52 = 32