The 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)
Let A be the number of adults and C be the number of children.
From the problem, we can write two equations:
A + C = 500 (equation 1, because 500 people are projected to attend)
10A + 5C = 3500 (equation 2, because the PTA wants to earn $3,500 from admission charges)
From equation 1, we can write A = 500 - C.
Substituting the value of A in equation 2, we get 10(500 - C) + 5C = 3500
Expanding and simplifying the equation, we get 5000 - 10C + 5C = 3500
Combining like terms, we get 5000 - 5C = 3500
Subtracting 5000 from both sides of the equation, we get -5C = -1500
Dividing both sides of the equation by -5, we get C = 300
Substituting the value of C in equation 1, we get A + 300 = 500
Subtracting 300 from both sides of the equation, we get A = 200
Thus, the PTA needs 200 adults and 300 children to attend the carnival for them to reach their goal of $3,500.