math question for school

Question

A total of 397 tickets were sold for the school play. They were either adult tickets or student tickets. There were 53

 fewer student tickets sold than adult tickets. How many adult tickets were sold?

Answer 1

For this question, it's helpful to set up an equation. Let's call student tickets the variable s and adult tickets the variable a. There are 53 more adult tickets (a) than student tickets (s), so a = s + 53.

In an equation, we could set the total (397 tickets) equal to the parts (adult and student tickets), which would be 397 = s + a. We said that

a = s + 53, so 397 = s + (s + 53). Then, through simplifying this, the final equation would be 397 = 2s + 53.

Now, we want to find a. So, first we must subtract 53 from both sides, which leaves us with 344 = 2s. Since s and 2 are connected through multiplication, we must divide 2 from both sides, which leaves us with

172 = s. We said a = s + 53, so a = 172 + 53.

Therefore, a = 225, so 225 adult tickets were sold.