If X Z Y + X Y Z = Y Z X. Find the three digits

Question

If  X Z Y + X Y Z = Y Z X. Find the three digits

crashonce · Answer

If X, Y and Z are different it would be very hard

ganeshie8 · Answer

100X + 10Z + Y + 100X + 10Y + Z = 100Y+10Z + X

199X + Z  = 89Y

crashonce · Answer

wait so can they be the same?

anonymous · Answer

https://in.answers.yahoo.com/question/index?qid=20140115062325AAtN1kl

ganeshie8 · Answer

so basically 199X + Z must be a multiple of 89

anonymous · Answer

000,954

crashonce · Answer

954 doesnt work..

ganeshie8 · Answer

199X + Z = 89Y

21X+Z = 89k

clearly, X must be atleast 4 :
X = 4, gives Z = 5

ganeshie8 · Answer

Other values of X give Z > 9, so the only solution is X=4, Z=5

crashonce · Answer

does that work though @ganeshie8

ganeshie8 · Answer

X=4, Z=5 

plug them in :
199X + Z = 89Y

you get Y = (199*4+5)/89 = 9

ganeshie8 · Answer

so X = 4, Y = 9, Z = 5 has to work, right ?

crashonce · Answer

oh yea it does sorry

anonymous · Answer

495+459=954

crashonce · Answer

yya

souvik · Answer

i dont get this part...@ganeshie8 (Moderator)
199X + Z = 89Y
to
21X+Z = 89k

ganeshie8 · Answer

oh, ive skipped a step there, see if below looks fine :

199X + Z = 89Y

21X + 178X + Z = 89Y

21X + Z = 89Y - 178X
             = 89(Y-2X)
             = 89k