SOLUTION: Please help with this question: Sara asked her grandfather how old he was. He replied that the two digits in his ageg are the ages of her brother and sister. If they are added t

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Question 124021: Please help with this question:
Sara asked her grandfather how old he was. He replied that the two digits in his ageg are the ages of her brother and sister. If they are added together to his, the sum is 83. How old is Sara's grandfather?
Thank you for your help.

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
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