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 \( a \) be the number of adults and \( c \) be the number of children. We have the following two equations based on the problem:

1. The total number of attendees: \[ a + c = 500 \]

2. The total amount of money earned from admissions: \[ 10a + 5c = 3500 \]

Now, we can solve these equations simultaneously.

From the first equation, we can express \( c \) in terms of \( a \): \[ c = 500 - a \]

Now, substitute this expression for \( c \) into the second equation: \[ 10a + 5(500 - a) = 3500 \] Distributing the 5: \[ 10a + 2500 - 5a = 3500 \]

Combine like terms: \[ 5a + 2500 = 3500 \]

Subtract 2500 from both sides: \[ 5a = 1000 \]

Now, divide by 5 to solve for \( a \): \[ a = 200 \]

Now substitute \( a \) back into the equation for \( c \): \[ c = 500 - a = 500 - 200 = 300 \]

Thus, the solution is: \[ \text{200 adults and 300 children} \]

Final answer: 200 adults; 300 children