A test has 10 questions worth 100 points in total. The test consists of multiple choice questions, which at worth 4 points each, and open-response questions, which are worth 12 points each. How many multiple choice questions are on the test

Given:

A test has 10 questions worth 100 points.

Points of each multiple choice question = 4

Points of each open-response question = 12

To find:

The number of multiple choice questions.

Solution:

Let x be the number of multiple choice questions and y be the open-response questions.

According to the question,

Total question :         ...(i)

Total points :      ...(ii)

Form (i), we get

        ...(iii)

Putting this in (ii), we get

Dividing both sides by -8, we get

Since x is the number of multiple choice questions, so it cannot be a faction value.

Therefore, the number of multiple choice questions in test are either 2 or 3.

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