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's assume the number of adults attending the carnival is A and the number of children attending is C.
From the problem, we know that adults are charged $10 for admission and children are charged $5 for admission. So, the total amount earned from adults would be 10A and the total amount earned from children would be 5C.
According to the problem, the PTA wants to earn a total of $3,500 from admission charges. So, we can set up the equation:
10A + 5C = 3,500 .....(1)
We also know that the total number of people attending the carnival is 500. So, we can set up another equation:
A + C = 500 .....(2)
To solve the system of equations, we can use substitution method. Rearrange equation (2) to solve for A:
A = 500 - C
Now substitute this value of A in equation (1):
10(500 - C) + 5C = 3,500
5000 - 10C + 5C = 3,500
-5C = -1500
C = 300
Substitute this value of C back into equation (2):
A + 300 = 500
A = 500 - 300
A = 200
So, there need to be 200 adults and 300 children attending the carnival for the PTA to reach their goal of $3,500.