How many children and how many adults were admitted?

Question

The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 337 people entered the park, and the admission fees collected totaled 968.000 dollars. How many children and how many adults were admitted?

Answer 1

This is a system of equations.  We have two variables (the number of adults and the number of kids) so we need two equations that describe the relationship between these two variables.

 

adults + kids = 337 people

 

$4.00*adults + $1.50*kids = $968.00

 

translating these into algebra:

 

A + K = 337

4A + 1.5K = 968

 

There are a few different ways to solve the system of equations, but they usually involve trying to get rid of one of the variables temporarily, so that we can easily solve for the other one.  I'm going to do this with SUBSTITUTION.

 

A + K = 337, so  A = 337- K

 

Now I can substitute 337 - K for A in the other equation, because 337-K and A are EQUAL.

 

4A + 1.5K = 968

4(337-K) + 1.5K = 968

 

distribute the 4

1348-4K + 1.5K = 968

 

combine

1348-2.5K= 968

 

now solve for K.

-2.5K = 968 - 1348

-2.5K = -380

K = 152

 

So that means there were 152 kids at the park.  Knowing that, can you figure out how many adults there were?