Question

You will take a test with multiple choice questions and short answer questions. The multiple choice questions are worth 1 point and the short answer questions are worth 3 points. There is a total of 100 points on the test and 70 total questions. How many questions of each type? Set up a system and solve. Let x = number of multiple choice questions and y = number of short answer questions.

Answer 1

9514 1404 393

Answer:

• 15 short answer (3 points)
• 55 multiple choice (1 point)

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.