Question

Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket?

Answer 1

We can form two equations, let the price of a senior ticket be s and the price of a child ticket be c.
We have from day 1:
A: 3s + 9c = 75
And from day 2:
B: 8s + 5c = 67

Now we can rewrite A as:
A: 24s + 72c = 600
And can rewrite B as:
B: 24s + 15c = 201

Now A-B can be written as:
A-B: 57c = 399

So c = 7

Now substituting this back into A we get:
A: 3s + 63 = 75
A: 3s = 12

So s = 4

We have the price of a senior ticket is $4 and the price of a child ticket is $7