The solar 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 planted 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 the PTA to reach their goal of 3,500?
Let A be the number of adults and C be the number of children.
We know that A + C = 500 and 10A + 5C = 3500.
We can rewrite the first equation as C = 500 - A.
Substituting the second equation into the first equation, we get 10A + 5(500 - A) = 3500.
Distributing, we get 10A + 2500 - 5A = 3500.
Combining like terms, we get 5A + 2500 = 3500.
Subtracting 2500 from both sides, we get 5A = 1000.
Dividing both sides by 5, we get A = 200.
Substituting that value into the first equation, we get 200 + C = 500.
Subtracting 200 from both sides, we get C = 300.
Thus, 200 adults and 300 children need to attend the carnival to reach their goal of 3500 dollars. Answer: \boxed{200, 300}.