The Kelsey middle school PTA is planning carnival to raise money for the schools 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 five dollars for admission the PTA wants to earn $3500 from admission charges how many adults and how many children need to attend for the PTA to reach their goal of $3500?
Let x be the number of adults and y be the number of children attending the carnival.
From the problem, we know that:
x + y = 500 (1) (Since a total of 500 people are attending the carnival)
And:
10x + 5y = 3500 (2) (Since they want to earn $3500 from admission charges)
To solve the system of equations, we can multiply equation (1) by -5 and add it to equation (2) to eliminate y:
-5x - 5y = -2500
10x + 5y = 3500
-----------------
5x = 1000
x = 200
Substituting the value of x in equation (1), we get:
200 + y = 500
y = 500 - 200
y = 300
Therefore, there need to be 200 adults and 300 children attending for the PTA to reach their goal of $3500.