[tex]n-\text{the number}\\\\\dfrac{1}{2}n-\text{half of the number}\\\\\dfrac{1}{5}n-\dfrac{1}{5}\ \text{of the number}\\\\51-\text{the sum}\\\\\text{The equation:}\\\\n+\dfrac{1}{2}n+\dfrac{1}{5}n=51\qquad\text{multiply both sides by 10}\\\\10n+10\!\!\!\!\!\diagup^5\cdot\dfrac{1}{\not2_1}n+10\!\!\!\!\!\diagup^2\cdot\dfrac{1}{\not5_1}n=10\cdot51\\\\10+5n+2n=510\\\\17n=510\qquad\text{divide both sides by 17}\\\\\boxed{n=30}\\\\Answer:\ \boxed{The\ original\ number\ is\ 30}[/tex]
