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

Answer:

The price of 1 senior ticket = $8.

Step-by-step 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,

$\frac{-3S}{-3}=\frac{-24}{-3}$

$S=8$

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