The Kesling Middle School PTA is planning a carnival to raise money for the school’s art department. They 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 admission. The PTA wants to earn $3,500 from admission charges. How many adults and how many children need to attend for the PTA to reach their goal of $3,500?(1 point) adults; children
Let's assume that a represent the number of adults attending the carnival and c represent the number of children attending the carnival.
We can set up a system of equations to represent the information given:
a + c = 500 (Equation 1)
10a + 5c = 3500 (Equation 2)
We want to solve for a and c. We can rearrange equation 1 to solve for a:
a = 500 - c
Substitute this expression for a into equation 2:
10(500 - c) + 5c = 3500
Distribute:
5000 - 10c + 5c = 3500
Combine like terms:
-5c = -1500
Divide both sides by -5:
c = 300
Substitute this value for c back into equation 1 to solve for a:
a + 300 = 500
Subtract 300 from both sides:
a = 200
Therefore, there need to be 200 adults and 300 children attending the carnival for the PTA to reach their goal of $3,500.