The school that Trey goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold 6 senior citizen tickets and 12 child tickets for a total of $78. The school took in $88 on the second day by selling 12 senior citizen tickets and 7 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

$5 for a senior citizen

$4 for a child

Step-by-step explanation:

1. Approach

To solve this problem, one must first form a system of equations, based on the information given in the problem. Then one will solve the system of equations using the process of elimination. Finally, to find the other value, one can back solve, substitute the value of the other variable back in and find the value of the first variable.

2. Find the system of equations

Let (x) represent the price for a senior citizen ticket, and (y) represents the price for a child ticket.

Form an equation based on the given information;

6x + 12y = 78

12x + 7y = 88

3. Solve the system

The process of elimination is a method of solving a system of equations by multiplying both of the equations by a certain value such that when one adds the equations a variable eliminates. One can now solve this single- variable equation using inverse operations.

6x + 12y = 78     (*-2)

12x + 7y = 88

-12x - 24y = -156

12x + 7y = 88

- 17y = -68

Inverse operations,

-17y = -68

/(-17)

y = 4

4. Solve for the other variable

Now that one has the value of one of the variables, the other variable value can be found by substituting this variable value into one of the equations and solving for the other variable.

12x + 7y = 88

y = 4

Substitute,

12x + 7(4) = 88

Simplify,

12x + 28 = 88

Inverse operations,

12x + 28 = 88

       -28   - 28

12x = 60

/12     /12

x = 5