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.

The test contained 29 multiple choice questions and 7 essay questions.

Let x represent the number of multiple questions and y represent the number of essay questions.

Given that there are a total of 36 questions, hence:

x + y = 36    (1)

Also, the test is worth a total of 100 points, hence:

2x + 6y = 100   (2)

Solving equation 1 and 2 simultaneously gives:

x = 29, y = 7

Therefore the test contained 29 multiple choice questions and 7 essay questions.

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(a) 7 essays and 29 multiple questions

(b) Your friend is incorrect

Step-by-step explanation:

Represent multiple choice with M and essay with E.

So:

--- Number of questions

--- Points

Solving (a): Number of question of each type.

Make E the subject of formula in

Substitute 36 - M for E in

Collect Like Terms

Divide both sides by -4

Substitute 29 for M in

Solving (b): Can the multiple questions worth 4 points each?

It is not possible.

See explanation.

If multiple question worth 4 points each, then

would be:

Where x represents the number of points for essay questions.

Substitute 7 for E and 29 for M.

Subtract 116 from both sides

Make x the subject

Since the essay question can not have worth negative points.

Then, it is impossible to have the multiple questions worth 4 points

Your friend is incorrect.

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