How many of each ticket were sold?

Question

Chicago zoo charges $22 for adult tickets and $15 for children. There were 732 tickets sold which resulted in a profit of $12,912. How many of each ticket were sold?

Answer 1

Here's what we know:

a + c = 732 (there were 732 tickets sold to adults & children)

22a + 15c = 12912 (total profit of the tickets is $12,912)

 

Let's use substitution here by isolating a variable in the first equation. Let's isolate c by subtracting a to both sides:

c = 732 - a

 

Plug in the value into the other equation:

22a + 15(732 - a) = 12912

Distribute:

22a + 10980 - 15a = 12912

Simplify:

7a + 10980 = 12912

Subtract 10980:

7a = 1932

Divide by 7:

a = 276

 

c = 732 - 276

c = 456

 

Check:

22 * 276 + 15 * 456 = 12912

6072 + 6840 = 12912

12912 = 12912