Answer
The number is 120.
Work Step by Step
step 1
Let x represent the unknown number in the problem.
step 2
"$ 60\%$ of a number" = $\displaystyle \frac{30}{100}\cdot x=0.6x$
" ... $ 60\%$ of the number is added to the number" = $x+0.6x$
" the result is $192$" is written as " = $192$"
step 3
The equation is
$x+0.6x=192$
step 4
$ x+0.6x=192\qquad$/simplify LHS
$1.6x=192\qquad/\div 1.6$
$x=\displaystyle \frac{192}{1.6}=\frac{1920}{16}=120$
The number is $120$.
step 5
Check the solution in the original wording of the problem.
When 60% of 120, ($\displaystyle \frac{60}{100}\cdot 120=72),$
is added to the number (72+120)
the result is 192.
OK.
