Question

Last year, 3/5 of the outing club for girls, but this year the number of boys doubled and six new girls joined. There are now as many boys in the club as there are girls. How many members did the club have last year?

Answer 1

Answer:

There were 30 members in the outing club last year.

Step-by-step explanation:

Let the number of members in the club last year be 'x'.

Given:

3/5 of the members last year were girls.

This year, the number of boys doubled and six new girls joined.

This year, the number of boys is equal to the number of girls.

Consider last year:

Now, as per question:

Number of girls last year = $\frac{3}{5}x$

So, number of boys last year is equal to the difference of total number of members and number of girls.

Framing in equation form, we get:

Number of boys = $x-\frac{3}{5}x=\frac{5x-3x}{5}=\frac{2}{5}x$

Consider this year:

Number of boys doubled. So, new number of boys is given as:

New number of boys = 2 × Last year number

New number of boys = $2(\frac{2x}{5})=\frac{4x}{5}$

Number of girls joined = 6. So, new number of girls is given as:

New number of girls = Last year + 6

Nuw number of girls = $\frac{3x}{5}+6$

Now, as per question:

New number of boys = New number of girls

$\frac{4x}{5}=\frac{3x}{5}+6\\\\\frac{4x}{5}-\frac{3x}{5}=6\\\\\frac{4x-3x}{5}=6\\\\\frac{x}{5}=6\\\\x=6\times 5\\\\x=30$

So, there were 30 members in the outing club last year.