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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
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1 answer

Let's denote the number of adults as \( a \) and the number of children as \( c \). We have two equations based on the information provided:

  1. The total number of people attending is 500: \[ a + c = 500 \]

  2. The total earnings from admission charges should be $3,500: \[ 10a + 5c = 3500 \]

Now we can solve these equations simultaneously.

First, let's solve the first equation for \( c \): \[ c = 500 - a \]

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

Expanding this gives: \[ 10a + 2500 - 5a = 3500 \]

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

Now, subtracting 2500 from both sides: \[ 5a = 1000 \]

Dividing by 5 gives: \[ a = 200 \]

Now that we have the number of adults, we can find the number of children using the equation \( c = 500 - a \): \[ c = 500 - 200 = 300 \]

Thus, the PTA needs:

  • 200 adults
  • 300 children

So the final answer is: 200 adults; 300 children.