SOLUTION: Jack is married to Jill. their son, junior, asked each of them to reveal their ages. Juniors parents decided to tell him but in the form of a puzzle. Jack told Junior, "If you reve

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Question 637479: Jack is married to Jill. their son, junior, asked each of them to reveal their ages. Juniors parents decided to tell him but in the form of a puzzle. Jack told Junior, "If you reverse the digits in my age, you'll get your mothers age."
Jill told her son, "the sum of my age and your dad's age is equal to 11 times the difference in our ages"
"Wait a minuet," said junior, "I cant figure out your ages with just those two clues"
"You're right" said Jack "Remember that I am older than you're mother."
What are the ages of Jack and Jill?
Found 2 solutions by Edwin McCravy, DrBeeee:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Jack is married to Jill. Their son, junior, asked each of them to reveal their ages. Junior's parents decided to tell him but in the form of a puzzle. Jack told Junior, "If you reverse the digits in my age, you'll get your mother's age."
Let a = the tens digit of Jack's age
Let b = the ones digit of Jack's age
Then Jack's age = 10a+b
Jill's age = 10b+a

Jill told her son, "the sum of my age and your dad's age is equal to 11 times the difference in our ages...said Jack "Remember that I am older than your mother." 
(10b+a) + (10a+b) = 11[(10a+b)-(10b+a)]

10b + a + 10a + b = 11[10a+b-10b-a]

        11b + 11a = 11(9a-9b)

        11b + 11a = 99a - 99b

             110b = 88a

Divide both sides by 22

               5b = 4a

Divide both sides by a

             %285b%29%2Fa = %284a%29%2Fa

             %285b%29%2Fa = 4

Divide both sides by 5

             b%2Fa = 4%2F5

The only possibility for a and b both being digits is

a = 5 and b = 4

So Jack is 54 and Jill is 45.

Checking: The sum of their ages is 99 and the
difference of their ages is 9, and 99 is 11 times 9.


Edwin

Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Let m = Mom's age = ab
Let d = Dad's age = ba > ab
Numerically (assuming Dad < 100 years old)
m = 10a + b
d = 10b + a
Then
m + d = 10a + b + 10b +a = 11a + 11b = 11*(a+b)
d - m = (10b + a) - (10a + b) = 9b - 9a = 9*(b - a)
Since m+d = 11*(d-m) we have
11*(a+b) = 11*9*(b-a) or
(a+b) = 9*(b-a)
This is satisfied when
(a+b) = 9
(b-a) = 1
Solving this pair of equations for a and b yields
a = 4
b = 5
Therefore the Dad is 54 and Mom is 45.
Are they correct? Let's see.
Is 45 the reverse of 54? Yes
Is [(45+54) = 11*(54-45)]?
Is [99 = 11*9]?
Is [99=99]? Yes