Question

The Family Fine Arts Center charges $20 per adult and $13 per senior citizen for its performances. On a recent weekend evening when 514 people paid admission, the total receipts were $7886. How many who paid were senior citizens?

Answer 1

342.

Explanation:

Let x represent the number of adults and y represent the number of senior citizens.

We have been given that on a recent weekend evening 514 people paid for the admission. We can represent this information in an equation as:

`x+y=514...(1)`

We have been given that the Family Fine Arts Center charges $20 per adult and $13 per senior citizen for its performances.

The cost of x adult tickets would be
`20x` and cost of y senior citizen tickets would be
`13y`.

We are also told that total receipts were $7886 on a recent weekend evening. We can represent this information in an equation as:

`20x+13y=7,886...(2)`

From equation (1), we will get:

We can represent this information in an equation as:

`x=514-y`

Substitute this value in equation (2) as:

`20(514-y)+13y=7,886`

`10,280-20y+13y=7,886`

`10,280-7y=7,886`

`10,280-10,280-7y=7,886-10,280`

`-7y=-2394`

`(-7y)/(-7)=(-2394)/(-7)`

`y=342`

Therefore, 342 senior citizens paid for the art center.