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Question Number 74191 by Mr. K last updated on 20/Nov/19

9Y4 +75X Z86 −−−− W387 find X+Y+Z+W.

$$\:\:\:\:\mathrm{9}{Y}\mathrm{4} \\ $$$$+\mathrm{75}{X} \\ $$$$\:\:\:\:{Z}\mathrm{86} \\ $$$$−−−− \\ $$$${W}\mathrm{387} \\ $$$${find}\:{X}+{Y}+{Z}+{W}. \\ $$

Answered by MJS last updated on 20/Nov/19

904+10y+750+x+100z+86=1000w+387 x+10y+100z+1353=1000w x+3=10 ⇒ x=7 10y+100z+1360=1000w y+6=10 ⇒ y=4 100z+1400=1000w z+4=10 ⇒ z=6 2000=1000w ⇒ w=2 x+y+z+w=19

$$\mathrm{904}+\mathrm{10}{y}+\mathrm{750}+{x}+\mathrm{100}{z}+\mathrm{86}=\mathrm{1000}{w}+\mathrm{387} \\ $$$${x}+\mathrm{10}{y}+\mathrm{100}{z}+\mathrm{1353}=\mathrm{1000}{w} \\ $$$${x}+\mathrm{3}=\mathrm{10}\:\Rightarrow\:{x}=\mathrm{7} \\ $$$$\mathrm{10}{y}+\mathrm{100}{z}+\mathrm{1360}=\mathrm{1000}{w} \\ $$$${y}+\mathrm{6}=\mathrm{10}\:\Rightarrow\:{y}=\mathrm{4} \\ $$$$\mathrm{100}{z}+\mathrm{1400}=\mathrm{1000}{w} \\ $$$${z}+\mathrm{4}=\mathrm{10}\:\Rightarrow\:{z}=\mathrm{6} \\ $$$$\mathrm{2000}=\mathrm{1000}{w}\:\Rightarrow\:{w}=\mathrm{2} \\ $$$${x}+{y}+{z}+{w}=\mathrm{19} \\ $$

Commented by Mr. K last updated on 20/Nov/19

why x+3=10?

$${why}\:{x}+\mathrm{3}=\mathrm{10}? \\ $$

Commented by MJS last updated on 20/Nov/19

because 1353 has to get 1000w 1353+zyx=1000w 1353 ^( ) zyx === w000

$$\mathrm{because}\:\mathrm{1353}\:\mathrm{has}\:\mathrm{to}\:\mathrm{get}\:\mathrm{1000}{w} \\ $$$$\mathrm{1353}+{zyx}=\mathrm{1000}{w} \\ $$$$\mathrm{1353} \\ $$$$\:\:^{\:\:} {zyx} \\ $$$$=== \\ $$$${w}\mathrm{000} \\ $$

Commented by malwaan last updated on 20/Nov/19

because 4 + X + 6 = 17

$$\boldsymbol{{because}}\:\mathrm{4}\:+\:\boldsymbol{{X}}\:+\:\mathrm{6}\:=\:\mathrm{17} \\ $$

Answered by MJS last updated on 20/Nov/19

09y4 075x 0z86 === w387 same as 0904 00y0 0750 000x 0086 0z00 === w387 same as 1740 0zyx === w387 sane as 1353 0zyx === w000 same as w000 −1353 ==== 0zyx

$$\mathrm{09}{y}\mathrm{4} \\ $$$$\mathrm{075}{x} \\ $$$$\mathrm{0}{z}\mathrm{86} \\ $$$$=== \\ $$$${w}\mathrm{387} \\ $$$$ \\ $$$$\mathrm{same}\:\mathrm{as} \\ $$$$ \\ $$$$\mathrm{0904} \\ $$$$\mathrm{00}{y}\mathrm{0} \\ $$$$\mathrm{0750} \\ $$$$\mathrm{000}{x} \\ $$$$\mathrm{0086} \\ $$$$\mathrm{0}{z}\mathrm{00} \\ $$$$=== \\ $$$${w}\mathrm{387} \\ $$$$ \\ $$$$\mathrm{same}\:\mathrm{as} \\ $$$$ \\ $$$$\mathrm{1740} \\ $$$$\mathrm{0}{zyx} \\ $$$$=== \\ $$$${w}\mathrm{387} \\ $$$$ \\ $$$$\mathrm{sane}\:\mathrm{as} \\ $$$$ \\ $$$$\mathrm{1353} \\ $$$$\mathrm{0}{zyx} \\ $$$$=== \\ $$$${w}\mathrm{000} \\ $$$$ \\ $$$$\mathrm{same}\:\mathrm{as} \\ $$$$ \\ $$$$\:\:\:{w}\mathrm{000} \\ $$$$−\mathrm{1353} \\ $$$$==== \\ $$$$\:\:\:\:\:\mathrm{0}{zyx} \\ $$

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