Question

Because their posters were so popular, Ms. Ironperson and Mr. Thoro decided to hold a class on how to make a super hero capes. Tickets were sold to cover the costs of the materials for each cape.
The admission fee for children was $2.00 and $4.50 for adults. 3250 people showed up and $9625 was collected.

How many adults and children attended the class?

If x denotes the number of children and y denotes the number of adults, what are the equations needed to solve this problem?

Answer 1

Answer:

2,000 children attended and 1,250 adults attended.

The equations needed to solve these problems are:

$x+y=3250\\2.00x+4.50y=9625$

Step-by-step explanation:

First, set up a system of equations.  Let "x" equal the number of children who attended the class and let "y" equal the number of adults who attended the class.

Our two equations to use to solve this problem are:

$x+y=3250\\2.00x+4.50y=9625$

Then, I took the first equation and I isolated the x-variable:

$x+y=3250\\x+y-y=3250-y\\x=3250-y$

Then, I substituted (3250-y) in for the x-variable in the second equation and I solved for "y":

$2.00x+4.50y=9625\\2.00(3250-y)+4.50y=9625\\6500-2.00y+4.50y=9625\\6500+2.50y=9625\\6500-6500+2.50y=9625-6500\\2.5y=3125\\\frac{2.5y}{2.5}=\frac{3125}{2.5}\\ y=1250$

Next, I substituted the y-value that I got in for the y-variable in the first equation:

$x+y=3250\\x+1250=3250\\x+1250-1250=3250-1250\\x=2000$

Finally, now that I have found both the x-value and the y-value, I will use the values to check  in both of my equations:

Equation 1:

$x+y=3250\\2000+1250=3250\\3250=3250$

It works for Equation 1.

Equation 2:

$2.00x+4.50y=9625\\2.00(2000)+4.50(1250)=9625\\4000+5625=9625\\9625=9625$

It works for Equation 2.

Therefore, the values work.

That means that 2000 children attended the class and 1250 adults attended the class.