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Anastasy [175]
2 years ago
11

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

Mathematics
1 answer:
Ad libitum [116K]2 years ago
6 0

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:

M + E= 36 --- Number of questions

2M + 6E = 100 --- Points

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

Make E the subject of formula in M + E= 36

E = 36 - M

Substitute 36 - M for E in 2M + 6E = 100

2M + 6(36 - M) = 100

2M + 216 - 6M = 100

Collect Like Terms

2M - 6M = 100 - 216

-4M = - 116

Divide both sides by -4

M = \frac{-116}{-4}

M = 29

Substitute 29 for M in E = 36 - M

E = 36 - 29

E = 7

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

It is not possible.

See explanation.

If multiple question worth 4 points each, then

2M + 6E = 100 would be:

4M + xE = 100

Where x represents the number of points for essay questions.

Substitute 7 for E and 29 for M.

4 * 29 + x * 7 = 100

116 + 7x = 100

Subtract 116 from both sides

116-116 + 7x = 100 -116

7x = 100-116

7x = -16

Make x the subject

x = -\frac{16}{7}

Since the essay question can not have worth negative points.

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

<em>Your friend is incorrect.</em>

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