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

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

We know that the total attendance will be 500 people, so:
x + y = 500

We also know that the PTA wants to earn $3,500 from admission charges, so:
10x + 5y = 3500

Now we can solve the system of equations:
x + y = 500
10x + 5y = 3500

Multiplying the first equation by 5, we get:
5x + 5y = 2500

Subtracting this new equation from the second equation, we get:
5x = 1000
x = 200

Now we can substitute this value back into the first equation to solve for y:
200 + y = 500
y = 300

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