Question

The school production of​ 'Our Town' was a big success. For opening​ night, 323 tickets were sold. Students paid ​$3.50 ​each, while​ non-students paid ​$5.50 each. If a total of $ 1354.50 was​ collected, how many students and how many​ non-students attended?
The number of students was
nothing. ​(Simplify your​ answer.)
The number of​ non-students was
nothing. ​(Simplify your​ answer.)

Answer 1

Answer:

112 non-students and 211 students

Step-by-step explanation:

So, we have two kinds of paying attendees, students (x) and non-students (y).

We know that all together, they were 323, so x + y = 323

We know the base formula to calculate the total entry money goes like:

3.5x + 5.5y = 1354.50 (X students paid $3.50 and Y non-students paid $5.50)

Now, from the first equation, we can isolate x as x = 323 - y

Let's place this value of x in the second equation:

3.5 (323 - y) + 5.5y = 1354.50

1130.50 - 3.5y + 5.5y = 1354.50

2y = 224

y = 112

So, 112 non-students paid $5.50.

From first equation, we have:

x + y = 323

x + 112 = 323

x = 211

And 211 students paid $3.50.

We can verify with the second equation:

3.5x + 5.5y = 1354.50

3.5 * 221 + 5.5 * 112 = 1354.50

738.50 + 616 = 1354.50

1354.50 = 1354.50