## Thinking Mathematically (6th Edition)

The number is $140$.
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.