**Question**

**Solution**

Let us write down the given information in
a Ratio diagram.

As you can see, we have ratios with
different units, which seems difficult to solve. However, notice that the number of boys
stayed the same throughout. We know that
the LCM of 6 and 7 is 42. So let us use
another type of unit, say “heart” units, with the number of boys corresponding
to 42 of these units. This can be done by
multiplying the first column by 7 and multiplying the second column by 6. This is what we get

With the “heart” units, now it is very
obvious that one “heart” is equivalent to 2.
From here we easily deduce that the number of boys is 84.

**Commentary**

This is a type of “problem” where one
quantity (the number of boys) is kept constant while another (the number of
girls) changes, giving rise to different ratios. It is similar to the "Boys, Girls and Party" problem, and you can certainly solve this problem using the
bridging method shown there. However,
here we exploit the fact that the number of boys stayed the same, and we use
the LCM to create a common type of unit (“heart” unit). Once this is done, we can easily compare the
number of girls using this common unit, and then the problem unravels. Don’t you © hearts?

Anyway, talking about authenticity in
mathematics problems ... the number of boys is already 84, if you work out the
total i.e. including the girls, you get ... (Do This Yourself). Won’t you find this class a little too
crowded?

The person who set this question should probably have moved the pupils to the auditorium, yes?

The person who set this question should probably have moved the pupils to the auditorium, yes?

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