"A mathematics club consists of 80 members. 65% of the members are boys."

What can you calculate from here? The number of boys. You have learnt how to calculate percentages of a number in primary school, so I won't go deep into the workings.

Number of boys
= 65% of the members
= 65% of 80 members
= 65% x 80
= 52

Number of girls
= 80 - 52
= 28

So at this point, we know that there are 52 boys and 28 girls.

--------------------------------------------------------

Now, here's the difficult part. The new members does not consist of the same number of boys and girls. In fact, there's one more new girl than new boy.

What I'm going to do for now (temporarily) is to "pretend" that one new girl joins the new club first. Only one girl. The remaining girls and boys will join the club at a later time.

--------------------------------------------------------

The moment this first new girl comes in,

number of boys = 52
number of girls = 29

Now that this has been settled, there will be an equal number of girls and boys coming in. The modified story would now sound like this.

"A mathematics club consists of 52 boys and 29 girls. After an equal number of boys and girls joined the club, 60% of the members are boys."

Sounds familiar?

[Except that normally it's something like "there will be four times as many..." or things like that]

--------------------------------------------------------

Now, 60%, or 3/5, of the final number of members are boys. Then 40%, or 2/5 of the final number of members are girls. In short, there are 3 units of boys and 2 units of girls. The difference will be 1 unit.

However, if an equal number of boys and girls join the club, the difference between the number of boys and the number of girls will remain unchanged.

Difference
= 52 - 29
= 23

So, 1 unit = 23
2 units = 46

So, there are 46 girls now.

[There will be 69 boys now as well; this means that based on the original story, 17 new boys join the club and 18 new girls join the club]

So let me summarise the workings.

Number of boys at first
= 65% x 80
= 52

Number of girls at first
= 80 - 52
= 28

After 1 new girl joins in first, number of girls
= 28 + 1
= 29

Difference between number of boys and number of girls
= 52 - 29
= 23

60% --> 3 units (out of 5) of boys
40% --> 2 units (out of 5) of boys

[You can draw a model at this point, but please take note...as Arnold has rightfully pointed out, Sec 1 is a time where you start to transition from models to algebraic methods, and once you enter Sec 2, models are no longer seen]

1 unit = 23 members
2 units = 46 members

So, there are 46 girls now.

Whether you love algebra or hate it, I have to include the alternative algebraic method as well for you to compare against the "primary school method".

Here's the algebraic method.

Number of boys
= 65% x 80
= 52

Number of girls
= 80 - 52
= 28

Let there be x new boys and (x + 1) new girls joining.

Final number of boys = 52 + x
Final number of girls = 29 + x

If 60% of the total number of members are boys, then 40% are girls, so their corresponding ratio is 3 : 2. Note that ratios can are commonly written as fractions (3/2) at the secondary level.

Then, we have

(52 + x) / (29 + x) = 3 / 2

Cross multiplying (an important technique to learn),
2 (52 + x) = 3 (29 + x)
104 + 2x = 87 + 3x
104 - 87 = 3x - 2x
17 = x

So, 17 new boys and 18 new girls join the club.

Final number of girls
= 28 + 18
= 46