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I-think-of-a-two-digit-number-The-sum-of-the-digits-is-9-When-the-number-is-reversed-and-subtracted-from-the-original-the-result-is-45-Find-the-original-number-




Question Number 26207 by pieroo last updated on 22/Dec/17
I think of a two digit number.The sum of the digits is 9.  When the number is reversed and subtracted from the  original, the result is 45. Find the original number
$$\mathrm{I}\:\mathrm{think}\:\mathrm{of}\:\mathrm{a}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{number}.\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{is}\:\mathrm{9}. \\ $$$$\mathrm{When}\:\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{reversed}\:\mathrm{and}\:\mathrm{subtracted}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{original},\:\mathrm{the}\:\mathrm{result}\:\mathrm{is}\:\mathrm{45}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{original}\:\mathrm{number} \\ $$
Answered by peileng8802 last updated on 22/Dec/17
let x be tens   y be ones  x+y=9  (10x+y)− (10y+x)= 45    x=9−y  10x+y−10y−x=45  9x−9y=45  x−y=5  9−y−y=5           −2y= −4                  y=2               x= 7  ∴x=7   , y=2
$$\mathrm{let}\:\mathrm{x}\:\mathrm{be}\:\mathrm{tens}\:\:\:\mathrm{y}\:\mathrm{be}\:\mathrm{ones} \\ $$$$\mathrm{x}+\mathrm{y}=\mathrm{9} \\ $$$$\left(\mathrm{10x}+\mathrm{y}\right)−\:\left(\mathrm{10y}+\mathrm{x}\right)=\:\mathrm{45} \\ $$$$ \\ $$$$\mathrm{x}=\mathrm{9}−\mathrm{y} \\ $$$$\mathrm{10x}+\mathrm{y}−\mathrm{10y}−\mathrm{x}=\mathrm{45} \\ $$$$\mathrm{9x}−\mathrm{9y}=\mathrm{45} \\ $$$$\mathrm{x}−\mathrm{y}=\mathrm{5} \\ $$$$\mathrm{9}−\mathrm{y}−\mathrm{y}=\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:−\mathrm{2y}=\:−\mathrm{4} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}=\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}=\:\mathrm{7} \\ $$$$\therefore\mathrm{x}=\mathrm{7}\:\:\:,\:\mathrm{y}=\mathrm{2} \\ $$
Commented by pieroo last updated on 22/Dec/17
thanks boss
$$\mathrm{thanks}\:\mathrm{boss} \\ $$

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