Question 504017
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,
:
Let x = the 10s digit of Jacks age
Let y - the units digit
:

“If you reverse the digits in my age, you get your mother’s age.
J = 10x + y
M = 10y + x
:
Jill told her son, “The sum of my age and your dad’s age is equal to 11 times the difference in our ages.”
(10x+y) + (10y+x) = 11[(10x+y) - (10y+x)] 
10x + x + y + 10y = 11(10x - x - 10y + y
11x + 11y = 11(9x - 9y)
simplify, divide both sides by 11
x + y = 9x - 9y
y + 9y = 9x - x
10y = 8x
simplify, divide both sides by 2
5y = 4x
y = {{{4/5}}}x
the only integer solution: x=5, y=4
:
Jack is 54, Mom is 45
;
:
See if that works out in the statement:
"The sum of my age and your dad’s age is equal to 11 times the difference in our ages.”
54 + 45 = 11(54-45)
99 = 11(9)