Question 198253
I change the 20% into 80%,when reducing, because it makes it easier to work with.
ie{{{(x-.2x)=(1-.2)x=.8x}}}

A student first reduced a certain number (henseforth called x) by 20%...
{{{.8x}}}
...and then increased it again by 20%.
{{{1.2(.8x)}}}
If the difference between the last number and the original number was 8...
{{{1.2(.8x)-.8x=8}}}
{{{.96x-.8x=8}}}
{{{.16x=8}}}
{{{x=50}}}
...then the original number was:
{{{50}}}