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?
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 the number of people attending is A + C = 500.
We also know that the admission charge for adults is $10 and for children is $5.
So the total amount earned from adults is 10A and from children is 5C.
We need to find the values of A and C that satisfy the following equation:
10A + 5C = 3500.
From the information given, we get the equation:
A + C = 500.
We can solve this system of linear equations to find the values of A and C that satisfy both equations.
We can rewrite the second equation as:
C = 500 - A.
Substitute this expression for C into the first equation:
10A + 5(500 - A) = 3500.
Simplify:
10A + 2500 - 5A = 3500.
Combine like terms:
5A + 2500 = 3500.
Subtract 2500 from both sides:
5A = 1000.
Divide both sides by 5:
A = 200.
Substitute this value of A back into the equation A + C = 500:
200 + C = 500.
Subtract 200 from both sides:
C = 300.
So, the number of adults needed to reach the goal of $3,500 is 200 and the number of children needed is 300.
Adults: 200
Children: 300