Question

Admission to a movie theater is $6 for children and $14 for adults. On a certain day, 63 people bought tickets at the theater and $530 was collected. How many children's tickets were sold and how many adult's tickets were sold

Answer 1

19 adults

44 children

Explanation:

Given

Represent Children with C and Adults with A

So, we have:

`6C + 14A = 530`

`A + C = 63`

Required

Determine the values of A and C

Make A the subject in
`A + C = 63`

`A = 63 - C`

Substitute 63 - C for A in the first equation

`6C + 14(63 - C) = 530`

`6C + 882 - 14C = 530`

Collect Like Terms

`6C - 14C = 530 - 882`

`-8C = -352`

`8C = 352`

Solve for C

`C = 352/8`

`C = 44`

Recall that:

`A = 63 - C`

Substitute 44 for C

`A = 63 - 44`

`A = 19`