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28 February, 01:57

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.)

+1
Answers (1)
  1. 28 February, 02:31
    0
    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
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