Question

A number half of that number and 1/5 of that number added the result is 51 what is the original number

Answer 1

`n-\text{the number}\\\\(1)/(2)n-\text{half of the number}\\\\(1)/(5)n-(1)/(5)\ \text{of the number}\\\\51-\text{the sum}\\\\\text{The equation:}\\\\n+(1)/(2)n+(1)/(5)n=51\qquad\text{multiply both sides by 10}\\\\10n+10\!\!\!\!\!\diagup^5\cdot(1)/(\\ot2_1)n+10\!\!\!\!\!\diagup^2\cdot(1)/(\\ot5_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}`