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:
Let the number of adults attending be A and the number of children attending be C.
From the information given, we know that:
A + C = 500 (1) (since a total of 500 people are attending)
And from the admission charges, we know that:
10A + 5C = 3500 (2) (since the adult admission fee is $10 and the child admission fee is $5, and the PTA wants to earn $3,500)
To find the values of A and C, we can solve these two equations simultaneously.
Multiplying equation (1) by 5, we get:
5A + 5C = 2500 (3)
Now we can subtract equation (3) from equation (2):
10A + 5C - (5A + 5C) = 3500 - 2500
5A = 1000
A = 200
Substituting A = 200 into equation (1), we can find C:
200 + C = 500
C = 300
Therefore, the number of adults needed for the PTA to reach their goal is 200 and the number of children needed is 300.