Answer
The number is 25.
Work Step by Step
step 1
Let x represent the unknown number in the problem.
step 2
"$ 20\%$ of itself" = $\displaystyle \frac{20}{100}\cdot x=0.2x$
" ... x is decreased by $ 20\%$ of itself" = $x-0.2x$
" the result is 20" is written as " = 20"
step 3
The equation is
$x-0.2x=20$
step 4
$ x-0.2x=20\qquad$/simplify LHS
$0.8x=20\qquad/\div 0.8$
$x=\displaystyle \frac{20}{0.8}=\frac{200}{8}=25$
The number is $25$.
step 5
Check the solution in the original wording of the problem.
The number (25),
decreased by 20% of 25,
($\displaystyle \frac{20}{100}\cdot 25=5),$
(25-5=20) gives the result 20.
OK.
