Question

a local theater is showing an anímated movie. They charge $5 per ticket for a child and $12 per ticket for an adult. They sell a total of 342 tickets and make a total of $2,550. We want to try to find out how many of each type of ticket They sold. Let C represent the number of children's tickets sold and A represent the number of adults tickets sold. write an equation that represents the fact that 342 total tickets were sold.write an equation representing the fact that they made a total of $2550Solve the system you created in (A) and (B) by the system of elimination

Answer 1

C + A = 342 (the equation that represents the fact that 342 total tickets were sold)

5C + 12A = 2550 (the equation representing the fact that they made a total of $2550)

120 Adult tickets and 222 children tickets were sold

Step-by-step explanation:

The cost of ticket per child = $5

let the number of children = C

The cost per ticket for Adult = $12

let the number of adult = A

Total tickets sold = 342

number of children + number of adult = 342

C + A = 342 ....(1) (This is the equation that represents the fact that 342 total tickets were sold)

Total amount generated from selling 342 tickets = $2550

cost of ticket per child (number of children) + cost per ticket for Adult (number of adult) = 2550

5(C) + 12(A) = 2550

5C + 12A = 2550 ....(2) (the equation representing the fact that they made a total of $2550)

Using elimination method:

To eliminate any of the variable, the coefficient of the variable have to be the same in both equations.

let's eliminate C. To do this, we will muliply equation (1) by 5:

5C + 5A = 342(5)

5C + 5A = 1710 ...(1*)

combining both equations:

5C + 5A = 1710 ...(1*)

5C + 12A = 2550 ....(2)

Both have same coefficient now. Subtract equation (1) from (2):

5C - 5C + 12A - 5A = 2550 - 1710

7A = 840

A = 840/7

A = 120

Substitute for A in equation (1):

C + 120 = 342

C = 342 - 120

C = 222

120 Adult tickets and 222 children tickets were sold