Find the price of a senior citizen ticket?

Question

The school that Luis goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior tickets and 1 child’s ticket for a total of $38. The school took in $52 on the second day by selling 3 senior tickets and 2 child’s tickets. Find the price of a senior ticket?

Answer 1

Let's use the variable s to represent the cost on one senior ticket and the variable c represent the cost of one child ticket.

Now we can write two equations based on the info given in the problem:

3s + 1c = 38

3s + 2c = 52

These equations can be solved using elimination. Multiply the first equation by -1:

3s + 1c = 38 becomes -3s - 1c = -38

3s + 2c = 52

Now combine the two equations to find the value of c:

-3s - 1c = -38

3s + 2c = 52

1c = 14

The cost of one child ticket is $14

Use either equation to find the value of s. Using the second equation, substitute 14 for c:

3s + 2c = 52

3s + 2•14 = 52

3s + 28 = 52

3s + 28 - 28 = 52 - 28

3s = 24

3s/3 = 24/3

s = 8

The cost of one senior ticket is $8.