Question

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

Answer 1

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 : $x+y=10$         ...(i)

Total points : $4x+12y=100$      ...(ii)

Form (i), we get

$y=10-x$         ...(iii)

Putting this in (ii), we get

$4x+12(10-x)=100$

$4x+120-12x=100$

$-8x=100-120$

$-8x=-20$

Dividing both sides by -8, we get

$x=\dfrac{-20}{-8}$

$x=2.5$

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.