Question

Your teacher is giving you a test worth 100 points containing 40 questions. There are two point and to

ur point questions on the test. How many of each type of question are on the test?

Answer 1

There are 30 two point questions and 10 four point questions on the test.

Explanation:

Given:

Your teacher is giving you a test worth 100 points containing 40 questions. There are two point and four point questions on the test.

Now, to find number of each type of question are on the test.

Let the two point questions be
`x`.

And let the four point questions be
`y`.

So, total questions:

`x+y=40.`.........( 1 )

⇒
`y=40-x.`

Now, total number of points of the questions on the test:

`2x+4y=100.`

Substituting the value of
`y`:

⇒
`2x+4(40-x)=100`

⇒
`2x+160-4x=100`

⇒
`160-2x=100`

Adding both sides by
`2x` we get:

⇒
`160=100+2x`

Subtracting both sides by 100 we get:

⇒
`60=2x`

Dividing both sides by 2 we get:

⇒
`30=x`

⇒
`x=30`.

The number of two point questions = 30.

Putting the value of
`x` in the equation ( 1 ) we get:

`30+y=40.`

Subtracting both sides by 30 we get:

⇒
`y=10.`

The number of four point questions = 10.

Therefore, there are 30 two point questions and 10 four point questions on the test.