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?

Number of 2-point questions = 30

Number of 4-point questions = 10

Step-by-step explanation:

Let the number of 2 point questions =

Let the number of 4 point questions =

Sum equation:

Total number of questions can be given by =

Total number of questions = 40

So, we have :

Points equation:

Total points for number of 2 point question =

Total points for number of 4 point question =

Total points in the test can be given by =

Total points in the test = 100

So, we have :

So, the system of equations is:

A)

B)  

Rearranging equation A, to solve for in terms of

Subtracting both sides by

Substituting value of we got from A into equation B.

Using distribution.

Simplifying.

Subtracting both sides by 160.

Dividing both sides by -2.

We can plugin in the rearranged equation A to get value of

∴

Thus, number of 2-point questions = 30

Number of 4-point questions = 10

the answer is  

a.

4,624π mm2

step-by-step explanation: