The kesling Middle School PTA is planning a carnival to raise money for the schools 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 $3500?

Question

The kesling Middle School PTA is planning a carnival to raise money for the schools 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 $3500?

Answer 1

Let's represent the number of adults attending as "A" and the number of children attending as "C".

Given:
A + C = 500
10A + 5C = 3500

Using the first equation, we can express A in terms of C:
A = 500 - C

Now substitute A into the second equation:
10(500 - C) + 5C = 3500
5000 - 10C + 5C = 3500
5000 - 5C = 3500
-5C = -1500
C = 300

Now we can substitute C back into the equation to find the number of adults:
A = 500 - 300
A = 200

Therefore, 200 adults and 300 children need to attend for the PTA to reach their goal of $3500.