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?

Respuesta :

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:

[tex]x+y=514...(1)[/tex]

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 [tex]20x[/tex] and cost of y senior citizen tickets would be [tex]13y[/tex].

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

[tex]20x+13y=7,886...(2)[/tex]

From equation (1), we will get:

We can represent this information in an equation as:

[tex]x=514-y[/tex]

Substitute this value in equation (2) as:

[tex]20(514-y)+13y=7,886[/tex]

[tex]10,280-20y+13y=7,886[/tex]

[tex]10,280-7y=7,886[/tex]

[tex]10,280-10,280-7y=7,886-10,280[/tex]

[tex]-7y=-2394[/tex]

[tex]\frac{-7y}{-7}=\frac{-2394}{-7}[/tex]

[tex]y=342[/tex]

Therefore, 342 senior citizens paid for the art center.

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