Question

The school that Anthony goes to is selling tickets for a choir concert. On the first day of ticket sales his school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. What is the price of a senior citizen ticket?

Answer 1

A senior citizen costs $8

Explanation:

Represent senior citizens with S and children with C.

The first day is represented as:

`3S + C = 38`

The second day is represented as:

`3S + 2C = 52`

Required

Solve for C and S

Make C the subject in the first equation

`C = 38 - 3S`

Substitute 38 - 3S for C in the second equation

`3S + 2(38 - 3S) = 52`

`3S + 76 - 6S = 52`

Collect Like Terms

`3S - 6S = 52 - 76`

`- 3S = -24`

Divide through by -3

`S = 8`

Recall that:
`C = 38 - 3S`

`C = 38 - 3 * 8`

`C = 38 - 24`

`C = 14`

Hence, a senior citizen costs $8