The counseling middle school PTA is planning a carnival to raise money for the schools are department they estimate that the event will be very popular and they were 500 people attend. They plan to charge adults 10 and children five dollars for admission the PTA wants to earn $3500 for admission charge is how many doors 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.
The total number of people attending the carnival is given as x + y = 500.
The total amount earned from adults is 10x and from children is 5y.
The total amount earned is given as 10x + 5y.
Given, the PTA wants to earn $3500, so we have the equation:
10x + 5y = 3500
From the first equation x + y = 500, we can solve for x:
x = 500 - y
Substitute x = 500 - y into the second equation:
10(500 - y) + 5y = 3500
5000 - 10y + 5y = 3500
5000 - 5y = 3500
-5y = -1500
y = 300
Substitute the value of y back into x = 500 - y:
x = 500 - 300
x = 200
Therefore, the PTA needs 200 adults and 300 children to attend the carnival in order to reach their goal of $3500.