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?
___ adults; ___ children
Let x be the number of adults and y be the number of children attending the carnival.
From the given information, we can create a system of equations:
1. x + y = 500 (total number of people attending)
2. 10x + 5y = 3500 (total revenue needed)
We can solve this system of equations using substitution or elimination method.
From equation 1, we have x = 500 - y
Substitute x = 500 - y into equation 2:
10(500 - y) + 5y = 3500
5000 - 10y + 5y = 3500
-5y = -1500
y = 300
Substitute y = 300 into x = 500 - y
x = 500 - 300
x = 200
Therefore, the PTA needs 200 adults and 300 children to attend the carnival in order to reach their goal of $3,500.