The Willis 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 400 people attend. They plan to charge adults $8 and children $3 for admission. The PTA wants to earn $2,500 from admission charges. How many adults and how many children need to attend for the PTA to reach their goal of $2,500?

Question

The Willis 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 400 people attend. They plan to charge adults $8 and children $3 for admission. The PTA wants to earn $2,500 from admission charges. How many adults and how many children need to attend for the PTA to reach their goal of $2,500?

Answer 1

Let's denote the number of adults attending the carnival as A and the number of children attending as C.

Given:
A + C = 400 (total number of people attending)
8A + 3C = 2500 (total amount earned from admission charges)

Now we can solve this system of equations using substitution or elimination method.

From the first equation, we can rearrange to get:
A = 400 - C

Substitute this into the second equation:
8(400 - C) + 3C = 2500
3200 - 8C + 3C = 2500
-5C = -700
C = 140

Now that we have the number of children attending, we can find the number of adults:
A = 400 - 140
A = 260

Therefore, the PTA needs 260 adults and 140 children to attend the carnival in order to reach their goal of $2,500.