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
To solve this problem, let's use algebra to represent the situation.
Let's assume that the number of adults attending is represented by 'A' and the number of children attending is represented by 'C'.
The total revenue from adults attending would be $10 * A and the total revenue from children attending would be $5 * C.
Given that the PTA wants to earn $3,500 from admission charges, the equation representing the total revenue is:
10A + 5C = 3500
We also know that there will be a total of 500 people attending, so the total number of attendees is:
A + C = 500
Now, we need to solve these two equations simultaneously.
10A + 5C = 3500
A + C = 500
Rearranging the second equation to solve for A, we get:
A = 500 - C
Substitute this into the first equation:
10(500 - C) + 5C = 3500
5000 - 10C + 5C = 3500
5000 - 5C = 3500
-5C = -1500
C = 300
Now that we know the number of children attending is 300, we can substitute this back into the equation A = 500 - C:
A = 500 - 300
A = 200
Therefore, the number of adults attending should be 200 and the number of children attending should be 300 for the PTA to reach their goal of $3,500.