Posted by Anonymous on Tuesday, October 25, 2011 at 7:10pm.
"My husband's age," remarked a lady the other day, "is represented by the figures of my own age reversed. He is my senior, and the difference between our ages is oneeleventh of their sum."
10x + y = husband's age
10y + x = wife's age
(10x+y)  (10y+x) = ((10x+y) + (10y+x))
10x + y  10y  x = (10x + y + 10y + x)
9x  9y = (11x + 11y)
9x  9y = 11(x + y)
9x  9y = x + y
9x  x = 9y + y
8x = 10y
x = y
x = 1.25y
How do you get the answer Husband is 54, wife is 45. I understand how to set it up and solve it, now how do i figure out their ages?

Algebra 2  Steve, Wednesday, October 26, 2011 at 5:17am
(10x+y)  (10y+x) = ((10x+y) + (10y+x))/11
11(9x  9y) = 11x + 11y
9x  9y = x + y
8x = 10y
4x = 5y
Both x and y are integers less than 10
Since 5 divides 5y, 5 must divide 4x. That means x = 5. Thus, y=4.
Answer This Question
Related Questions
 maths  a teen age boy wrote his own age after his father's from this new four ...
 Math  Jack is married to Jill. Their son, Junior, asked each of them to reveal ...
 statistics  5. The ages of husbands and wives in a community were found to have...
 statistics  5. The ages of husbands and wives in a community were found to have...
 Prealgerbra  Ok, It is riddle. Jack is married to Jill. There son wants to ...
 Simultaneous equation  Ann is older than Betty. Their ages in years are such ...
 Algebra  I am 6 years older than my wife. Our twins go to the local ...
 algebra  The difference between the ages of two friends is 2 years. The sum of ...
 math  The range of the of the ages of the Glee club officers is 5. this means ...
 algebra  art's age is two thirds cal's age, and bob is three years older than ...
More Related Questions