How many multiple choice questions are on the te

Question

A test has twenty questions worth 100 points. The test consists of true/false questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?

Answer 1

Let x = the number of true/false questions and y = the number of multiple choice questions.  Since we have two unknowns, we need two equations:

• The test has 20 questions: x+y = 20, so x = 20-y
• A test is worth 100 points  It has true/false questions worth 3 points each and multiple choice questions worth 11 points each:  3x + 11y = 100

 

Since x = 20-y, let's substitute 20-y in place of x in the second equation:

      3x + 11y = 100

      3(20-y) + 11y = 100

      60 - 3y + 11y = 100

      8y = 40

 

      y = 5

 

There are 5 multiple choice questions and 20-5 = 15 true/false questions.