## Thinking Mathematically (6th Edition)

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.