The solution:

It's solutions like this that convinced me that maths was essentially illogical. But see what you think.

I’m going to refer to the guppies as “g”, the angelfish as “a” and the catfish as “c”.

We know there are 198 altogether.

g + a + c = 198

There are 4 times as many guppies as angelfish, so 4 lots of angelfish is the same as the number of guppies

4a = g

And also, we know that there are 6 more angelfish than catfish, so catfish is angelfish minus 6

a – 6 = c

If we substitute the g and c into the first equation, we get

4a + a + a – 6 = 198

Tidying this up gives us 6a = 204 (we’ve added 6 to both sides of the equation )

So a = 34 (angelfish)

We know that catfish is angelfish minus 6, so catfish = 28

We also there are 4 times as many guppies as angelfish, so guppies = 136

Just to check we need g + a + c = 198

34 + 28 + 136 does equal 198.

So the answer is 28.