Please answer this question.

Question

A biology test is worth 100 points and has 36 questions.

a. Multiple-choice questions are worth 2 points each and essay questions are worth 6 points each. How many questions of each type are on the test?

b. Your friend says that it is possible for the multiple-choice questions to be worth 4 points each. Is your friend correct? Explain.

Answer 1

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.

Answer 2

a) I tried: 30 multiple-choice and 6 essay 30 x 2 = 60.....6 x 6 =36....total is 96 points

29 multiple-choice and 7 essay 29 x 2 = 58....7 x 6 = 42...total is 100 points

b) I used logic to prove the friend is wrong....he doubled the value of the multiple-choice....so

there has be be a least one essay: 35 x 4 = 140....1 x 6 = 6....total 146 points

146 is the lowest possible amount of points