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we-have-three-digit-number-like-XYZ-that-X-Y-Z-16-if-we-replace-X-by-Z-then-it-will-be-changed-to-ZYX-number-that-ZYX-XYZ-594-find-XYZ-number-




Question Number 192047 by sciencestudentW last updated on 06/May/23
we have three digit number like XYZ  that X+Y+Z=16, if we replace X by Z  then it will be changed to ZYX number   that ZYX=XYZ−594  find XYZ number.
$${we}\:{have}\:{three}\:{digit}\:{number}\:{like}\:{XYZ} \\ $$$${that}\:{X}+{Y}+{Z}=\mathrm{16},\:{if}\:{we}\:{replace}\:{X}\:{by}\:{Z} \\ $$$${then}\:{it}\:{will}\:{be}\:{changed}\:{to}\:{ZYX}\:{number}\: \\ $$$${that}\:{ZYX}={XYZ}−\mathrm{594} \\ $$$${find}\:{XYZ}\:{number}. \\ $$
Answered by AST last updated on 08/May/23
100Z+10Y+X−100X−10Y−Z=−594  ⇒99Z−99X=−594⇒Z−X=−6⇒X−Z=6  ⇒(X,Z)=(9,3),(8,2),(7,1)  ⇒Y=4,6 or 8  ⇒XYZ=943, 862 or 781
$$\mathrm{100}{Z}+\mathrm{10}{Y}+{X}−\mathrm{100}{X}−\mathrm{10}{Y}−{Z}=−\mathrm{594} \\ $$$$\Rightarrow\mathrm{99}{Z}−\mathrm{99}{X}=−\mathrm{594}\Rightarrow{Z}−{X}=−\mathrm{6}\Rightarrow{X}−{Z}=\mathrm{6} \\ $$$$\Rightarrow\left({X},{Z}\right)=\left(\mathrm{9},\mathrm{3}\right),\left(\mathrm{8},\mathrm{2}\right),\left(\mathrm{7},\mathrm{1}\right) \\ $$$$\Rightarrow{Y}=\mathrm{4},\mathrm{6}\:{or}\:\mathrm{8} \\ $$$$\Rightarrow{XYZ}=\mathrm{943},\:\mathrm{862}\:{or}\:\mathrm{781} \\ $$
Commented by sciencestudentW last updated on 07/May/23
great
$${great}\: \\ $$

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