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he 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

1 answer

To solve this problem, we need to set up a system of equations based on the information provided.

Let:

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

From the problem, we have the following information:

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

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

Now we can solve these equations step by step.

Step 1: Solve the first equation for one of the variables

From the first equation: \[ c = 500 - a \]

Step 2: Substitute \( c \) in the second equation

Substituting \( c \) in the second equation: \[ 10a + 5(500 - a) = 3500 \]

Step 3: Simplify and solve for \( a \)

\[ 10a + 2500 - 5a = 3500 \] Combining like terms: \[ 5a + 2500 = 3500 \] Subtracting 2500 from both sides: \[ 5a = 1000 \] Dividing by 5: \[ a = 200 \]

Step 4: Find the value of \( c \)

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

Solution

Therefore, the solution is:

  • Adults: 200
  • Children: 300

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