Question

a theater charges x for adult tickets and y for child tickets. 2 adult tickets and 4 child tickets cost $48. 5 adult tickets and 2 child tickets cost $64. write and solve system a of equations to find the adult and child ticket prices.

Answer 1

The price of an adult ticket is $10 and the price of a child ticket is $7.

Step-by-step explanation:

To solve this problem, we can set up a system of equations.

Let x be the price of an adult ticket and y be the price of a child ticket.

From the given information, we can form the following equations:

2x + 4y = 48 (equation 1)

5x + 2y = 64 (equation 2)

To solve this system, we can use the method of substitution:

From equation 1, we can isolate x:

x = (48 - 4y)/2

Substitute this into equation 2:

5(48 - 4y)/2 + 2y = 64

Simplify and solve for y:

240 - 20y + 4y = 128

-16y = -112

y = 7

Substitute this value of y back into equation 1 and solve for x:

2x + 4(7) = 48

2x + 28 = 48

2x = 20

x = 10

Therefore, the price of an adult ticket is $10 and the price of a child ticket is $7.