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=(-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.