Margaret wants to score at least 74 points on her upcoming test. Fill in the blank questions, x, are worth 3 points each while multiple choice questions, y, are worth 1 point each. Use the graph below to identify one possible solution.

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

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.

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