Chloe charged for admission to her play on three different nights. Each night, a different number of people were in attendance, but remarkably, Chloe collected $541 each night. If the admission charges for each child and each adult were $9 and $17, respectively, how many people in total came to the three showing

9514 1404 393

Step-by-step explanation:

Your system of equations will be ...

  x + y = 70 . . . . . . . there are 70 total questions

  x + 3y = 100 . . . . . there are 100 total points

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We can use the first equation to write an expression for x that can be substituted into the second.

  x = 70 -y

  (70 -y) +3y = 100

  70 +2y = 100 . . . . . . collect terms

  2y = 30 . . . . . . . . . . subtract 70

  y = 15 . . . . . . . . . . . divide by 2

  x = 70 -15 = 55

The test has 15 short answer questions and 55 multiple-choice.