The kesling middle school PTA is planning a carnival to raise money for the schools art department they estimate that the event will be very popular and they will have 500 people attend. They plan to charge adults $10 in children five dollars per 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
_____ adults; ______ children
To calculate the number of adults and children needed to attend the carnival for the PTA to reach their goal of $3500, we can set up a system of equations.
Let x be the number of adults and y be the number of children attending the carnival.
From the information given, we know that the PTA plans to charge adults $10 and children $5 per admission. Therefore, the total revenue from admission charges can be calculated as:
10x (adults) + 5y (children) = 3500
We are also told that the PTA estimates 500 people will attend the carnival, so the total number of attendees can be expressed as:
x (adults) + y (children) = 500
Now, we can solve these two equations simultaneously to find the values of x and y:
10x + 5y = 3500
x + y = 500
To solve, we can first multiply the second equation by 5 to make the coefficients of y in both equations the same:
5x + 5y = 2500
Now, we can subtract the modified second equation from the first equation to eliminate y:
10x + 5y - 5x - 5y = 3500 - 2500
5x = 1000
x = 200
Now that we have found the number of adults (x = 200), we can substitute this value back into the second equation to find the number of children:
200 + y = 500
y = 300
Therefore, the PTA needs 200 adults and 300 children to attend the carnival in order to reach their goal of $3500.