Last Saturday, 1,750 people attended an event at Farway Gardens. The admission fee was $3.50 for children and $8.00 for adults. If the total amount of money collected at the event was $9,860, how many children and how many adults attended the event?

Let c be the number of children and a be the number of adults. Set up equations. Using the attendance of 1750 people, we can write: c+a=1750
Using the total money collected of 9860, we can write:
3.50c+8.00a = 9860
Solve by substitution. Using (1), we solve for a to obtain (3): a=1750—c
Substutute (3) to (2) and solve for c:
3.50c + 8.00(1750 — c) = 9860
3.50e+ 14000 — 8.00c = 9860
—4.50e= —4140
c=920
Solve for a using (3):
a=1750 — 920
a=830
So, there were 920 children and 830 adults.