The Kesling Middle School PTA is planning a carival 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 ear $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

adultsi
children

Answer 1

Let's denote the number of adults as \( x \) and the number of children as \( y \).

We have the following information:

1. The total number of attendees (adults + children) is 500: \[ x + y = 500 \]

2. The total revenue from admissions needs to be $3,500, where adults are charged $10 and children are charged $5: \[ 10x + 5y = 3500 \]

Now we have a system of equations:

1. \( x + y = 500 \) (Equation 1)
2. \( 10x + 5y = 3500 \) (Equation 2)

We can simplify Equation 2 by dividing everything by 5: \[ 2x + y = 700 \quad (Equation 3) \]

Now we can solve this system using substitution or elimination. Let's substitute Equation 1 into Equation 3.

From Equation 1, we can express \( y \) in terms of \( x \): \[ y = 500 - x \]

Now we substitute this into Equation 3: \[ 2x + (500 - x) = 700 \] \[ 2x + 500 - x = 700 \] \[ x + 500 = 700 \] \[ x = 200 \]

Now, substitute \( x \) back into Equation 1 to find \( y \): \[ 200 + y = 500 \] \[ y = 500 - 200 \] \[ y = 300 \]

So, the solution is:

• Number of adults \( x = 200 \)
• Number of children \( y = 300 \)

Thus, the PTA needs 200 adults and 300 children to attend to reach their goal of $3,500.