Question

Breana is selling tickets to a choral performance. On the first day of ticket sales, she sold 3 senior citizen tickets and 1 child ticket for a total of $38. Breana 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

The price of 1 senior ticket = $8.

Explanation:

Let C be the price of each child ticket and S be the price of each senior citizen ticket.

We have been given that on the first day of ticket sales, Breana sold 3 senior citizen tickets and 1 child ticket. So the price of 3 senior citizens will be 3S and price of 1 child ticket will be C.

As she got $38 from selling tickets on 1st day, so we can represent this information in an equation as:

`3S+C=38...(1)`

We are also told that on the second day Breana sold 3 senior citizen tickets and 2 child tickets. So the price of 3 senior citizens will be 3S and price of 2 child ticket will be 2C.

As she got $52 from selling tickets on 2nd day, so we can represent this information in an equation as:

`3S+2C=52...(2)`

To solve the price of each citizen ticket we will use substitution method to solve system of equations.

From equation (1) we will get,

`C=38-3S`

Substituting this value in equation (2) we will get,

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

`3S+76-6S=52`

Let us subtract 76 from both sides of our equation.

`3S+76-76-6S=52-76`

`3S-6S=52-76`

`-3S=-24`

Upon dividing both sides of our equation by -3 we will get,

`(-3S)/(-3)=(-24)/(-3)`

`S=8`

Therefore, the price of a senior ticket is $8.