Question: Rugby Players & Chess Players

I'm glad you like it!

The video solution already uses a lot of algebra to determine the answer.

We let x = TOTAL number of rugby players....

If we let x = the TOTAL number of Rugby players, then we know that:

(# of rugby players who play chess) + (# of rugby players who DON'T play chess) = x

We're told that 40% of ALL rugby players play chess.
In other words, the # of rugby players who play chess = 40% of x = 0.4x

We're also told that 40 students play rugby AND chess.

So, we can write: 40 + 0.4x = x

Does that help?

Cheers,
Brent

We're not actually saying that there are 100 students. We're using that figure because it's the easiest value to work with when answering questions involving percents.

Since we're asked to find a certain percent (and not a certain value) it doesn't really matter what value we assign the number of students. So, for example, if we said there are 600 students, we'd still arrive at the same final answer (try it and see what happens). In fact, we'd still arrive at the correct answer had we assigned an awful value (like 5.17) to the total number of students.

Does that help?

Cheers,
Brent

We're told that 40% of the students who play rugby do NOT play chess.

If we let x = the number of students who play rugby, then...
40% of x = the number of students who play rugby but do NOT play chess.

40% of x = 40/100 of x = (40/100)(x) = 0.4x

Does that help?

Cheers,
Brent

If a variable does not have a coefficient in front of it, then the coefficient is assumed to be 1.
For example:
x + x = 1x + 1x =
5x - x = 5x - 1x = 4x
1.7x - 0.4x = 1.3x

So for this question, x - 0.4x = 0.6x is the same as 1x - 0.4x = 0.6x
Does that help?