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?
Let's start by defining some variables:
- Let's call the number of adults attending "a"
- Let's call the number of children attending "c"
- We know that a + c = 500 (since 500 people are attending in total)
We also know that the PTA wants to earn $3,500 from admission charges. From our variable definitions, we can write an equation for the total amount earned:
10a + 5c = 3500
Now we have two equations with two unknowns. We can solve for either "a" or "c" in terms of the other variable. Let's solve for "a" in terms of "c":
a + c = 500
a = 500 - c
Now we can substitute this expression for "a" into the other equation:
10a + 5c = 3500
10(500-c) + 5c = 3500
5000 - 10c + 5c = 3500
-5c = -1500
c = 300
So we have found that 300 children will be attending. We can use the equation a + c = 500 to find the number of adults attending:
a + c = 500
a + 300 = 500
a = 200
Therefore, the PTA needs 200 adults and 300 children to attend in order to reach their goal of $3,500 from admission charges.
Let's assume the number of adults attending the carnival is 'A' and the number of children attending is 'C'.
We are given that the admission charge for adults is $10 and for children is $5.
The total amount earned from admission charges can be calculated using the following equation:
$10 * A + $5 * C = $3,500
We also know that the number of people attending the carnival (both adults and children) is 500.
So we can write another equation:
A + C = 500
Now we have a system of equations:
$10 * A + $5 * C = $3,500 ---(1)
A + C = 500 ---(2)
To solve this system of equations, we can use the substitution method.
Let's solve equation (2) for A:
A = 500 - C
Substitute this value of A in equation (1):
$10 * (500 - C) + $5 * C = $3,500
Simplifying the equation:
$5,000 - $10 * C + $5 * C = $3,500
Combine like terms:
-$5 * C = $3,500 - $5,000
-$5 * C = -$1,500
Divide both sides of the equation by -5:
C = -$1,500 / -$5
C = 300
Now substitute the value of C in equation (2):
A + 300 = 500
Subtract 300 from both sides of the equation:
A = 500 - 300
A = 200
Therefore, 200 adults and 300 children need to attend the carnival for the PTA to reach their goal of $3,500.
To solve this problem, let's assume the number of adults attending the carnival is 'x' and the number of children attending is 'y'.
Given that the number of attendees, x + y, is 500, we can write the equation:
x + y = 500
Since adults are charged $10 each and children are charged $5 each, the total amount of money earned from admission charges can be calculated as:
10x + 5y = 3500
Now we have a system of two equations with two unknowns:
x + y = 500
10x + 5y = 3500
We can solve this system using any method, but let's use substitution.
Rearranging the first equation, we can express y as:
y = 500 - x
Now we substitute this value of y in the second equation:
10x + 5(500 - x) = 3500
Expanding:
10x + 2500 - 5x = 3500
Combining like terms:
5x + 2500 = 3500
Subtracting 2500 from both sides:
5x = 1000
Dividing both sides by 5:
x = 200
Now we know that the number of adults, x, is 200. We can substitute this value back into the first equation to find the number of children:
200 + y = 500
y = 500 - 200
y = 300
Therefore, there need to be 200 adults and 300 children attending the carnival for the PTA to reach their goal of $3,500.