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

adults;
children

Answer 1

To find how many adults and children need to attend the carnival to reach the goal of $3,500, we can set up a system of equations.

Let:

• \( a \) = number of adults
• \( c \) = number of children

We have two equations based on the information provided:

1. The total number of attendees (adults + children) must equal 500: \[ a + c = 500 \]

2. The total admission income must equal $3,500: \[ 10a + 5c = 3500 \]

Now we can solve this system of equations.

First, from equation (1), we can express \( c \) in terms of \( a \): \[ c = 500 - a \]

Now, we can substitute this expression for \( c \) into equation (2): \[ 10a + 5(500 - a) = 3500 \]

Simplifying this equation: \[ 10a + 2500 - 5a = 3500 \] \[ 5a + 2500 = 3500 \] \[ 5a = 3500 - 2500 \] \[ 5a = 1000 \] \[ a = 200 \]

Now we can find \( c \): \[ c = 500 - a = 500 - 200 = 300 \]

Therefore, the PTA needs:

• Adults: 200
• Children: 300

So the answer is: 200 adults; 300 children.