Question 124021
X+Y+(10X+Y)=83
11X+2Y=83
10X+Y+X+Y=83 LET X=9 & Y=1
90+1+9+1=101 TOO LARGE LET Y=0
90+0+9+0=99 TOO LARGE. LET X=8 & Y=9
80+9+8+9=106 TOO LARGE. LET X=8 & Y=0
80+0+8+0=88 TOO LARGE. LET X=7 & Y=9
70+9+7+9=95 TOO LARGE. LET X=7 & Y=0
70+0+7+0=77 TOO SMALL. LET X=7 & Y=5
70+5+7+5=87. TOO LARGE. LET X=7 & Y=4
70+4+7+4=85. TOO LARGE. LET X=7 & Y=3
70+3+7+3=83. YAHOO WE FIND THE AGES OF THE BROTHER & SISTER.
THEY ARE 7 & 3.
GRAMPS AGE=7*10+3=73 
PROOF
11*7+2*3=83
77+6=83
83=83
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SETTING UP A TABLE FOR X & Y WE FIND THAT THE X DIGIT=7 & THE Y DIGIT=3
X=7
Y=3
PROOF:
11*7+2*3=83
77+6=83
10*7+3=73
7+3=10
73+10=83