What is the difference between $x\times 0.8$ and $x \div 1.2 ? $

Question

I came across this problem in a Khan Academy course:

There are 20% percent more goblins than wizards in a magic club. There are 120 goblins in the magic club.

To solve this problem I tried: $120 \times 0.8 = 96$. The correct answer was: $ 120\div 1.2 = 100$. What is the difference between $x\times 0.8$ and $x \div 1.2 ?$

Answer 1

There is a lack of symmetry to these sorts of problems.

Saying that there are 20% more goblins than wizards is not the same thing as saying that there are 20% fewer wizards than goblins.

I it aproximatly true for small percentages, and the bigger the changes get, the farther they diverge.

There are 20% more goblins than wizards.... means we need some guess about the number of wizards.

$1.2\cdot \text {wizards} = \text{goblins}$

Then we are given the number of goblins. and we can solve for the number of wizards.