Question

If the ratio of students toteachers on a committee of 21 members is 8 to 6 , how many members of the committee are students?

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

Number of students on the committee = 12

Step-by-step explanation:

What is a Ratio?

• The ratio is used to compare two quantities.

• It is the comparison between two numbers in relation to each other.

• It compares the numbers by division. The dividend in a division, i.e., the number that is being divided is known as the antecedent in a ratio. And the divisor, i.e, the number that is dividing is known as the consequent in a ratio.

Example: In a group of 50 people, if 30 are men and 20 are women, the ratio of men to women can be written as 30:20. Simplifying, we can write it as 3:2. Here 3 is the antecedent and 2 is the consequent.

This can be written as  $\frac{3k}{2k}$  where k is any constant.

Also, 3k + 2k = 5k

That is, the sum of the ratios is also a multiple of the constant.

Given:

Ratio of students to teachers in a committee = 8:6

Total members in the committee = 21

Find:

Number of students = ?

Solution:

Ratio of students to teachers in a committee = $8:6$

Number of students = $8k$

Number of teachers = $6k$

Total members in the committee = $8k + 6k = 14k$

We know that, total members of the committee = 21

∴ $14k =21$

⇒ $k=\frac{21}{14}$

⇒ $k =\frac{3}{2}$

Now, number of students = $8k$

                                           = $8 \times \frac{3}{2}$

                                           = $12$

Therefore, number of students on the committee = 12

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