Write and Solve system of equations and solve using one of the elimination method strategies

Question

There were 2000 people at the circus on Saturday. The audience included children and adults. The circus charged $5 for each child and $10 for each adult and made $14,000 that Saturday. How many children and how many adults were at the circus on Saturday?

Answer 1

NOTE that you could have solved for y:

y = 2000- x

and arrived at the same answer.

You could have also solved for x in the second equation

x = ( 14000 - 10y) / 5 = 2800 - 2y

or y

y = ( 14000 - 5x) / 10 = 1400 - (x/2)

Using these values in the other equation would probably be more complicated, and hence be more likely to lead to errors.

The use of substitution requires the user to be smart and seek the simplest path to the solution. It's really an art form.

Answer 2

The two variables we are trying to solve for are the number of children and the number of adults. Let x be the number of children and y be the number of adults. Because we have 2 variables we need at least 2 equations in order to solve.

We have 2 critical pieces of information: there were 2000 people present and the total revenue was 14000.

We can make one equation representing the number of people present.

x + y = 2000

and we can make another for how much money was made

5x + 10y = 14000.

I will use the substitution method to solve for x in terms of y.

x = 2000 - y

Then I substitute this representation of x into the second equation

5(2000 - y) + 10y = 14000

10000 -5y + 10y = 14000

5y = 4000

y = 800

Now we can solve for x because we know the value of y

x + 800 = 2000

x = 1200

So the final answer is 1200 children and 800 adults