"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?
(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.
To find out the ages of the husband and wife, we can use the information provided in the question and the equations derived from it. Let's break down the steps to solve the problem:
1. Start with the given equations:
- 10x + y = husband's age
- 10y + x = wife's age
2. Apply the information that the husband's age is represented by the figures of the wife's age reversed. This gives us the equation:
- x = y
3. Apply the information that the difference between their ages is one-eleventh of their sum. This gives us the equation:
- (10x + y) - (10y + x) = 1/11 * ((10x + y) + (10y + x))
4. Simplify the equation:
- 9x - 9y = 11x + 11y
5. Rearrange the equation by collecting the like terms:
- 9x - 11x = 9y + 11y
- -2x = 20y
6. Divide both sides of the equation by -2 to solve for x in terms of y:
- x = -10y
7. Substitute the value of x in terms of y into the equation x = y:
- -10y = y
8. Solve for y by moving all the terms with y to one side of the equation:
- -10y - y = 0
- -11y = 0
- y = 0
9. Substitute the value of y back into the equation x = y:
- x = 0
Thus, we find that the wife's age (x) is 0, which is not possible. Therefore, based on the equations provided, it seems that there may be an error in the problem statement or in the equations derived from it.