Question

Your teacher is giving you a test worth 100 points containing 40 problems. There are 2 point questions and 4 point questions on the test. How many of each type of question are on the test?

Answer 1

Number of 2-point questions = 30

Number of 4-point questions = 10

Explanation:

Let the number of 2 point questions =
`x`

Let the number of 4 point questions =
`y`

Sum equation:

Total number of questions can be given by =
`x+y`

Total number of questions = 40

So, we have :

`x+y=40`

Points equation:

Total points for
`x` number of 2 point question =
`2x`

Total points for
`y` number of 4 point question =
`4y`

Total points in the test can be given by =
`2x+4y`

Total points in the test = 100

So, we have :

`2x+4y=100`

So, the system of equations is:

A)
`x+y=40`

B)
`2x+4y=100`

Rearranging equation A, to solve for
`y` in terms of
`x`

Subtracting both sides by
`x`

`x+y-x=40-x`

`y=40-x`

Substituting value of
`y` we got from A into equation B.

`2x+4(40-x)=100`

Using distribution.

`2x+160-4x=100`

Simplifying.

`-2x+160=100`

Subtracting both sides by 160.

`-2x+160-160=100-160`

`-2x=-60`

Dividing both sides by -2.

`(-2x)/(-2)=(-60)/(-2)`

`x=30`

We can plugin
`x=30` in the rearranged equation A to get value of
`y`

`y=40-30`

∴
`y=10`

Thus, number of 2-point questions = 30

Number of 4-point questions = 10