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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.

Sagot :

MrRoyalidn

Answer:

(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:

[tex]M + E= 36[/tex] --- Number of questions

[tex]2M + 6E = 100[/tex] --- Points

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

Make E the subject of formula in [tex]M + E= 36[/tex]

[tex]E = 36 - M[/tex]

Substitute 36 - M for E in [tex]2M + 6E = 100[/tex]

[tex]2M + 6(36 - M) = 100[/tex]

[tex]2M + 216 - 6M = 100[/tex]

Collect Like Terms

[tex]2M - 6M = 100 - 216[/tex]

[tex]-4M = - 116[/tex]

Divide both sides by -4

[tex]M = \frac{-116}{-4}[/tex]

[tex]M = 29[/tex]

Substitute 29 for M in [tex]E = 36 - M[/tex]

[tex]E = 36 - 29[/tex]

[tex]E = 7[/tex]

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

It is not possible.

See explanation.

If multiple question worth 4 points each, then

[tex]2M + 6E = 100[/tex] would be:

[tex]4M + xE = 100[/tex]

Where x represents the number of points for essay questions.

Substitute 7 for E and 29 for M.

[tex]4 * 29 + x * 7 = 100[/tex]

[tex]116 + 7x = 100[/tex]

Subtract 116 from both sides

[tex]116-116 + 7x = 100 -116[/tex]

[tex]7x = 100-116[/tex]

[tex]7x = -16[/tex]

Make x the subject

[tex]x = -\frac{16}{7}[/tex]

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.

Raphealnwobiidn

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.

Find out more at: https://brainly.com/question/16763389

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