Answer
The number is $40$.
Work Step by Step
step 1
Let x represent the unknown number in the problem.
step 2
"$ 30\%$ of itself" = $\displaystyle \frac{30}{100}\cdot x=0.3x$
" ... x is decreased by $ 30\%$ of itself" = $x-0.3x$
" the result is $28$" is written as " = $28$"
step 3
The equation is
$x-0.3x=28$
step 4
$ x-0.3x=28\qquad$/simplify LHS
$0.7x=28\qquad/\div 0.7$
$x=\displaystyle \frac{28}{0.7}=\frac{280}{7}=40$
The number is $40$.
step 5
Check the solution in the original wording of the problem.
The number ($40$),
decreased by 30% of 40,
($\displaystyle \frac{30}{100}\cdot 40=12),$
($40-12$) gives the result $28$.
OK.
