how many adult tickets were sold?

Question

A total of 680

tickets were sold for the school play. They were either adult tickets or student tickets. There were 70

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

Answer 1

Shane,

Let's call the number of adult tickets sold "A" and the number of student tickets "S". If 680 tickets were sold and there are only two ticket options, adult and student, then the number of adult tickets plus the number of student tickets has to equal 680.

That looks like this -> A + S = 680

We know that there were 70 fewer student tickets sold than adult tickets. So that means when we subtract the number of student tickets from the number of adult tickets, we get 70.

That looks like this -> A - S = 70

We can rearrange either of our equations to solve for A. I will show you what that looks like for the second equation.

A - S = 70

+S +S

A = 70 + S

We then plug our equation for A into our first equation.

That looks like this -> A + S = 680 -> 70 + S + S = 680 -> 70 + 2S = 680

We can this solve this equation for S by adding 70 to each side and then dividing by 2.

70 + 2S = 680 -> 2S = 610 -> S = 305

-70 = -70 2 2

2S = 610

Plug the value of S (number of student tickets) into either equation to solve for A (number of adult tickets).

A + S = 680 -> A + 305 = 680 -> A = 375

or

A - S = 70 -> A - 305 = 70 -> A = 375

The answer is 375 adult tickets and 305 student tickets were sold.