Answer :
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:
[tex]3S+C=38...(1)[/tex]
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:
[tex]3S+2C=52...(2)[/tex]
To solve the price of each citizen ticket we will use substitution method to solve system of equations.
From equation (1) we will get,
[tex]C=38-3S[/tex]
Substituting this value in equation (2) we will get,
[tex]3S+2(38-3S)=52[/tex]
[tex]3S+76-6S=52[/tex]
Let us subtract 76 from both sides of our equation.
[tex]3S+76-76-6S=52-76[/tex]
[tex]3S-6S=52-76[/tex]
[tex]-3S=-24[/tex]
Upon dividing both sides of our equation by -3 we will get,
[tex]\frac{-3S}{-3}=\frac{-24}{-3}[/tex]
[tex]S=8[/tex]
Therefore, the price of a senior ticket is $8.
