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?

Answer 1

Let's start by defining some variables:
- Let's call the number of adults attending "a"
- Let's call the number of children attending "c"
- We know that a + c = 500 (since 500 people are attending in total)

We also know that the PTA wants to earn $3,500 from admission charges. From our variable definitions, we can write an equation for the total amount earned:
10a + 5c = 3500

Now we have two equations with two unknowns. We can solve for either "a" or "c" in terms of the other variable. Let's solve for "a" in terms of "c":
a + c = 500
a = 500 - c

Now we can substitute this expression for "a" into the other equation:
10a + 5c = 3500
10(500-c) + 5c = 3500
5000 - 10c + 5c = 3500
-5c = -1500
c = 300

So we have found that 300 children will be attending. We can use the equation a + c = 500 to find the number of adults attending:
a + c = 500
a + 300 = 500
a = 200

Therefore, the PTA needs 200 adults and 300 children to attend in order to reach their goal of $3,500 from admission charges.