The admission fee of a theater is $2.50 for adults and $1.25 for children. on a certain day, 700 people went to the theater for a concert and $1375 was collected. how many children and how many adults attended the concert?

There are two equations you can get from this.

2.5X+1.25Y=1375

X+Y=700

By solving for X, we can then plug the 2nd equation into the first equation.

X=700-Y

2.5(700-Y)+1.25Y=1375

1750-2.5Y+1.25Y=1375

375=1.25Y

Y=300

After we get the Y, we solve for the X.

300+X=700

X=400

There were 400 adults, and 300 children. A quick check proves this.

2.5(400)+1.25(300)=1375