Hello.

Let's let M = the number of Multiple choice problems and

N = the number of essay questions.

Since the multiple choice problems are worth 2 points and the essay questions are worth 6 points and the total number of points possible is 100, then:

2M + 6N = 100

Also, since there are 36 questions altogether, we can say that

M + N = 36

So, therefore

M = 36 - N

Now substitute M = 36 - N into the 1st equation above.

2(36 - N) + 6N = 100

72 - 2N + 6N = 100

4N = 100 - 72

4N = 28

N = 7

Now, since M = 36 - N, we can find that

M = 36 - 7 = 29

**So the number of multiple choice problems is 29 and the number of essay questions is 7.**

Now, check your answer:

2(29) + 6(7) = 58 + 42 = 100

The answer is correct.

For part b:

If the multiple choice problems are worth 4 points each and there are 29 multiple choice problems, then there would be 116 total points so it would not be possible.

Rebecca R.

10/24/20

Rw W.

Thank you so much. I got the equations right but when I solved it I kept getting the wrong answers because when I checked it and plugged it back in, it did not work. I finally figured out what I have done wrong after seeing your answers.10/24/20