Question

Four-fifths of the members of a club are female. Three-quarters of these females are over 20 years old. What fraction of the members of the club are females over 20 years old?​

Answer 1

Step-by-step explanation:

We've been given that 4/5th of the members of a club are females. Out of 4/5th of the females, 3/4th (or three quarters) of the females are over twenty years old.  

Now, we have to find the fraction of females over 20 years old in the whole club.

Let the number of members in the club be 'y'.

No: of members → y

No: of women → 4/5 y

3/4th of 4/5 females are over twenty years old. Therefore;

The Fraction of women over 20 years old in the whole club is;

Now, the fraction of the members of the club who are females over 20 years old is;

The total fraction of women over 20 years old in the club are:

Therefore, 3/5 th is your answer!

Hope you understood!

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Answer 2

Answer:

We've been given that 4/5th of the members of a club are females. Out of 4/5th of the females, 3/4th (or three quarters) of the females are over twenty years old.

Now, we have to find the fraction of females over 20 years old in the whole club.

Let the number of members in the club be 'y'.

No: of members → y

No: of women → 4/5 y

3/4th of 4/5 females are over twenty years old. Therefore;

The Fraction of women over 20 years old in the whole club is;

\begin{lgathered}\Longrightarrow \sf \dfrac{3}{4} \times \dfrac{4}{5} \ y \\ \\ \\\Longrightarrow \sf \dfrac{12}{20} \ y \\ \\ \\\Longrightarrow \sf \dfrac{3}{5} \ y \\ \\ \\\end{lgathered}

⟹

4

3

×

5

4

y

⟹

20

12

y

⟹

5

3

y

Now, the fraction of the members of the club who are females over 20 years old is;

The total fraction of women over 20 years old in the club are:

\begin{lgathered}\Longrightarrow \sf \dfrac{Fraction \ of \ women \ over \ 20 \ years \ old}{Total \ number \ of \ members}\\ \\ \\\Longrightarrow \sf \dfrac{\frac{3}{5} \ y}{y}\\ \\ \\\Longrightarrow \sf \dfrac{3}{5}\\ \\\end{lgathered}

⟹

Total number of members

Fraction of women over 20 years old

⟹

y

5

3

y

⟹

5

3

Therefore, 3/5th is your answer!

Hope you understood!