The Jurassic Zoo

Question

The Jurassic Zoo charges $15 for each adult admission and $3 for each child. The total bill for the 184 people from a school trip was $1068. How many adults and how many children went to the zoo?

Answer 1

Starting from scratch, think about how much 3 adult tickets would cost, for example. It would be 15+15+15 = 3*15 = $45. So, you can see a trend in this. If you let A be the number of adult tickets sold, the amount of money made would be 15*A. Applying this logic again for the children's tickets, you can let C be the number of children's tickets sold. So, the total amount of money made from selling C tickets would be 3*C. So, adding these up will give the total amount of money the zoo will make by selling A adult tickets and C children's tickets. In our example, this will give

(1) 1068 = 15A+3C

 

In addition to this, we know how many total tickets were sold. Though we still don't know how much of each, we do know that there are only two types of tickets. So the total number of adult tickets plus the children's tickets sold must be equal to 184, so we get

 

(2) 184 = A + C

 

We can use (2) to find a relationship between A and C. For example, we can see that (2) will give us 

 

(3) 184-C = A

 

Replacing the left hand side of (3) for A in (1) we get 

 

(4) 15(184-C)+3C = 1068

 

This equation is an equation of only C, and so through distributing the 15 to both terms in the parentheses and combining like terms one can get 

 

(5) 2760-12C = 1068

 

You can then solve (5) for C to get that 

 

(6) C = 141 

 

Then you can use (3) to see that 

 

(7) A = 43

 

Equations (6) and (7) are your answers!