System of Equations: How do I set up the equation?

Question

The admission fee at the fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and adults attended?

 

I'm doing system of equations (elimination), but I don't know how to set this up.

Answer 1

First, define your variables for the number of children and number of adults attended, since that's what we want to find out.

 

Let x = number of children

Let y = number of adults

 

Then use these variables to create two equations.  One equation will represent the total number of people attending.  The second equation will represent the total amount of money collected.

 

x + y = 2200                        eq1       -----> total number of people attending

 

1.50x + 4y = 5050               eq2       -----> total amount of money collected

 

 

You now have your equations.  Now just use the elimination method to solve for x and y.