The QC middle school PTA is planning a carnival to raise money for the schools art department they estimated the event will be very popular and that they will have 500 people attend. They put a charge adults $10 in children five dollars for admission the PTA wants to earn $3500 from admission charges how many adults and how many children need to attend with a PTA to reach their goal of $3500

Answer 1

Let x be the number of adults attending and y be the number of children attending.

The total amount earned from adults: $10x
The total amount earned from children: $5y
Total amount earned: $10x + $5y

Given that the PTA wants to earn $3500, we have the equation:

$10x + $5y = $3500

We also know that the total number of people attending is 500:

x + y = 500

We can solve the system of equations using substitution or elimination method.

Let's use the elimination method to solve:

$10x + $5y = $3500 (1)
x + y = 500 (2)

Multiply equation (2) by $5 to make the coefficients of y the same as in equation (1):

$5x + $5y = $2500 (3)

Now subtract equation (3) from equation (1):

$5x = $1000
x = 200

Now substitute x = 200 back into equation (2):

200 + y = 500
y = 300

Therefore, the PTA needs 200 adults and 300 children to reach their goal of $3500.