At the afternoon matinee movie, 3 adult tickets and 5 child tickets cost $44, and 5 adult tickets and 3 child tickets cost $52. Which two equations can be used to determine the price of each ticket? Let x represent the cost of an adult ticket and y represent the cost of a child ticket.

3x+5y=44

5x+3y=52

then create a system of equations

x = $8

y = $4

Step-by-step explanation:

x = cost of an adult ticket

y = cost of child ticket

Firstly, 3 adult tickets and 5 child tickets cost $44

That's 3x + 5y = 44

Also, 5 adult tickets and 3 child tickets cost $52

That's 5x + 3y = 52

Now combine both equations.

1. 3x + 5y = 44

2. 5x + 3y = 52

Multiply equation one by 5 and equation two by 3

We have

5 x 3x + 5 x 5y = 5 x 44

3 x 5x + 3 x 3y = 3 x 52

We have

15x + 25y = 220

15x + 9y = 156

Subtract equation 2 from 1

16y = 64

Divide both sides by 16

16y/16 = 64/16

y = 4

Now substitute 4 for y in any of the equations to get x. Using equation one, we have

3x + 5 (4) = 44

3x + 20 = 44

Subtract 20 from both sides

3x + 20 - 20 = 44 - 20

3x = 24

Divide both sides by 3

x = 24/3

x = 8

Therefore, adult's ticket cost $8 while children's ticket cost $4