I need a little help understanding this problem

Question

Admission tickets to a theater worth $.60 for adults and $.25 for children. Receipts for the day showed that 280 people attended and what $140 was collected. How many children attended that day?

Answer 1

Let's let A be the number of Adult tickets and C be the number of Children's tickets.

 

We know that there were a total of 280 people in attendance so A + C = 280 (Equation #1)

We also know that the total receipts for the day were $140 made up of $0.60 for adult tickets and $0.25 for children's tickets.  

0.6A + 0.25C = 140 (Equation #2)

Using the first equation, A + C = 280, we can solver for A and get A = 280 - C

We can use this A and substitute it into the 2nd equation like this.

 

0.6 (280-C) + 0.25C = 140

Using algebra to rearrange the terms and isolate C, we get.

168 - 0.6C + 0.25C = 140

-0.35C = -28

and finally C = 80

So there were 80 children's tickets sold (80 children in attendance) that day.