Question

The school production of 'Our Town' was a big success. For opening night, 466 tickets were sold. Students paid $1.50 each, while non-students paid $3.50 each. If a total of $1059.00 was collected, how many students and how many non-students attended?

Answer 1

To solve this, first we need to determine two different equations to represent the two values we need to know.

The sum of the number os students and non-students is equal to 466

If x = number of students and y = number of non-students, then:

x + y = 466

The total amount of money raised was $1059

1.5x = money from students tickets

3.5y = money for non-students tickets.

So, our equation would look like this:

1.5x + 3.5y = 1059

In order to solve the second equation, we have to solve the first equation for either x or y. Let's solve for x

x + y = 466

subtract y from both sides

x = 466 - y

We then replace x in the second equation with the x in terms of y

1.5x + 3.5y = 1059

Let's solve for y

1.5(466 - y) + 3.5y = 1059

699 - 1.5y + 3.5y = 1059

Let's combine the y's

699 + 2y = 1059

subtract 699 from both sides

2y = 1059 - 699

2y = 360

divide both sides by 2

y = 360/2

y = 180

Now we can replace y in the first equation with the value for y: 180

x + y = 466

x + 180 = 466

subtract 180 from both sides:

x = 466 - 180

x = 286

recall, we said let:

x = number of students

y = number of non-students

Therefore, We now know that the the number of students that attended is 286 and the number of non-students that attended is 180.