Answer
The number is $140$.
Work Step by Step
step 1
Let x represent the unknown number in the problem.
step 2
"$ 80\%$ of a number" = $\displaystyle \frac{80}{100}\cdot x=0.8x$
" ... $ 80\%$ of the number is added to the number" = $x+0.8x$
" the result is $252$" is written as " = $252$"
step 3
The equation is
$x+0.8x=252$
step 4
$ x+0.8x=252\qquad$/simplify LHS
$1.8x=252\qquad/\div 1.8$
$x=\displaystyle \frac{252}{1.8}=\frac{2520}{18}=140$
The number is $140$.
step 5
Check the solution in the original wording of the problem.
When 80% of 140, ($\displaystyle \frac{80}{100}\cdot 140=112),$
is added to the number (112+140),
the result is 252.
OK.
