The Kessling 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 the plan to charge adults $10 and children five dollars for admission the PTA wants to earn $3500 from admission charges how many adults and how many children need to attend for the PTA to reach their goal of $3500
Let:
A = number of adults
C = number of children
From the given information, we can set up two equations:
1. A + C = 500 (total number of attendees)
2. 10A + 5C = 3500 (total admission revenue)
From the first equation:
A = 500 - C
Substitute the value of A in the second equation:
10(500 - C) + 5C = 3500
5000 - 10C + 5C = 3500
5000 - 5C = 3500
-5C = -1500
C = 300
Now, substitute the value of C back into the first equation to find A:
A + 300 = 500
A = 200
Therefore, 200 adults and 300 children need to attend the carnival for the PTA to reach their goal of $3500.