SOLUTION: Ann, Barb and Cathy are all younger than 100. The sum of any two of their ages is the reverse of the digits of the remaining person's age. What are their ages? I was doing o.k.

Question 227184: Ann, Barb and Cathy are all younger than 100. The sum of any two of their ages is the reverse of the digits of the remaining person's age. What are their ages?
I was doing o.k. until I hit the reverse digits line:(
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Ann, Barb and Cathy are all younger than 100.
The sum of any two of their ages is the reverse of the digits of the remaining person's age. What are their ages?
:
We know one thing about the reversal of digits, the difference between the two numbers is always a multiple of nine.
So all three ages have to be multiples of nine.
:
This narrows our choice of numbers to:18,27,36,45,54,63,81.
The sums of any two will be a multiple of 9 also
:
After a couple false hopes, I chose A=18; B=45
18 + 45 = 63, reversing that: C=36
and B + C
45 + 36 = 81, reversing that: A=18
and A + C
18 + 36 = 54, reversing this: B=45
:
Ann is 18
Barb is 45
Cathy is 36
:
As far as writing an equation to solve this, it would be extremely complicated, not practical, at least that's my opinion which is probably is not worth much.
Anyway, to date, no one has ventured to solve this one Carl

RELATED QUESTIONS
Ann, Ben and Cathy have their birthdays today. The sum of their ages is 23. The product... (answered by ikleyn,mananth)

John is seven years younger than his sister Ann. The sum of their ages is 45. Find john's (answered by Boreal)

The ages of Ann and Greg is 34,Greg is 8years older than ann..what are their... (answered by macston)

solve: jon is 2 years younger than Ann. their current ages are prime numbers. next year... (answered by ankor@dixie-net.com)

ann is 5 years older than mary. the sum of their ages is 35 find ann's age and mary's... (answered by T-Maree)

Melissa is 5 years younger than Ann. In 6 years, the sum of their ages will be 35. How... (answered by ikleyn,MathTherapy)

Melissa is 5 years younger than Ann. In 6 years, the sum of their ages will be 35. How... (answered by josgarithmetic,MathLover1)

Melissa is 5 years younger than Ann. In 6 years, the sum of their ages will be 35 how old (answered by josgarithmetic)

Cathy is 16 years older than rob. The sum of their ages is 46. How old is... (answered by t0hierry)