Question

Systems of Linear Equations Unit Test The Kesling Middle School PTA is planning a carnival to raise money for the school's art departmentThey estimate that the event will be very popular and that they will have 500 people attend. They plan to charge adults $10 and children $5 for admissionThe PTA wants to $3,500 from admission chargesHow many adults and how many children need to attend for the PTA to reach their goal of $3,500? (1 point) 7 adults700 children

Answer 1

Let x be the number of adults attending and y be the number of children attending.

The total number of people attending is x + y = 500.

The total amount of money raised from adults is 10x and from children is 5y.

The total amount raised from both adults and children is 10x + 5y.

According to the problem, the total amount raised is $3,500, so:

10x + 5y = 3500

Now we also know that the total number of people attending is 500, so:

x + y = 500

We can solve this system of equations by substitution or elimination method.

Let's use the elimination method to solve the system:

From the second equation, we have y = 500 - x

Substitute y in the first equation:

10x + 5(500 - x) = 3500
10x + 2500 - 5x = 3500
5x + 2500 = 3500
5x = 1000
x = 200

Now we can substitute x back into the second equation to find y:

200 + y = 500
y = 300

Therefore, the PTA needs 200 adults and 300 children to attend the carnival in order to raise $3,500.