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 one-eleventh 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.

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