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)

Question

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

Answer 1

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

Given:
x + y = 500 (total number of people attending)
10x + 5y = 3500 (total revenue from admission charges)

Solving the two equations simultaneously:
1. Multiply the first equation by 10 to eliminate y:
10x + 10y = 5000

2. Subtract the first equation from the second equation:
10x + 5y - 10x - 10y = 3500 - 5000
5y = -1500
y = -300

Admission charges cannot be negative, therefore the number of children attending cannot be negative.

So, it is not possible to reach the PTA's goal of $3,500 with their admission charges plan.