At a movie theater, the price of 2 adult tickets and 4 child tickets is $48. The price of 5 adult tickets and 2 child tickets is $64. What is the ticket price for one adult and for one child?

The price for one adult is $10 while the price for one child is $7

Step-by-step explanation:

Let

price for an adult = a

price for a child = b

2a + 4b = 48(i)

5a + 2b = 64(ii)

make a subject of the formula in equation (i)

2a = 48 - 4b

divide through by 2

a = 24 - 2b

Insert the value of a in equation (ii)

5(24 - 2b) + 2b = 64

120  - 10b + 2b = 64

collect like terms

- 8b = 64 - 120

-8b = -56

divide both sides by -8

b = 7

insert the value of b in equation(i)

2a + 4(7) = 48

2a + 28 = 48

2a = 48 - 28

2a = 20

divide both sides by 2

a = 10

The price for one adult is $10 while the price for one child is $7

the answer to this question is yes