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

Answer:

342.

Step-by-step 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:

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

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

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

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

$-7y=-2394$

$\frac{-7y}{-7}=\frac{-2394}{-7}$

$y=342$

Therefore, 342 senior citizens paid for the art center.