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)

Question

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

Answer 1

Let x be the number of adults attending the carnival.

Thus, the number of children attending the carnival is 500 - x.
The total admission charges from adults is 10x and the total admission charges from children is 5(500 - x).
The total admission charges will be 10x + 5(500 - x) = $3,500.
Expanding the equation, we get 10x + 2500 - 5x = $3,500.
Combining like terms, we get 5x + 2500 = $3,500.
Subtracting 2500 from both sides, we get 5x = $1,000.
Dividing both sides by 5, we get x = 200.
Therefore, there should be 200 adults and 500 - 200 = 300 children attending the carnival. Answer: \boxed{200; 300}.

Answer 2

Let's solve the problem step-by-step. Let "a" represent the number of adults attending the carnival and "c" represent the number of children attending.

From the problem, we know that the admission charge for adults is $10 and for children is $5.

We are given that the PTA wants to earn $3,500 from admission charges. Therefore, we can set up the following equation:

10a + 5c = 3500

Now, we need to take into account the total number of people attending the carnival. We are given that there will be 500 people in total, so we have another equation:

a + c = 500

We have a system of equations:

10a + 5c = 3500
a + c = 500

We can solve this system of equations using substitution or elimination. Let's use the substitution method here.

First, solve the second equation for "a" in terms of "c":

a = 500 - c

Now substitute this expression for "a" into the first equation:

10(500 - c) + 5c = 3500

Simplify and solve for "c":

5000 - 10c + 5c = 3500
-5c = -1500
c = 300

Now substitute this value of "c" back into the second equation to solve for "a":

a + 300 = 500
a = 200

Therefore, there should be 200 adults and 300 children attending the carnival in order for the PTA to reach their goal of $3,500 in admission charges.