SOLUTION: a two digit number is 11 times its units digit. The sum of the digits is 12. find the number

Question 387213: a two digit number is 11 times its units digit. The sum of the digits is 12. find the number
Found 2 solutions by gwendolyn, Alan3354:
Answer by gwendolyn(128) (Show Source): You can put this solution on YOUR website!
Let X be the tens digit
Let Y be the units digit
The value of the two digit number is calculated as 10*X + Y, since X is the digit in the tens spot. Since this number is 11 times its units digit, then
10*X + Y = 11*Y
Subtract Y from both sides:
10*X + Y - Y = 11*Y - Y
10*X = 10*Y
Divide both sides by 10:

X = Y
(Which makes sense if you think about two-digit multiples of 11.)
The sum of the digits is 12, so:
X + Y = 12
Substitute the value of X from the first equation:
Y + Y = 12
2*Y = 12
Divide both sides by 2:

Y = 6
Substitute in the first equation for X:
X = 6
So, the two-digit number is 66
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Since it's divisible by 11, the tens and units digits are the same.
12/2 = 6
--> 66

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