The ages of a man and his wife are in a ratio of 6:5. 6 years from now, their ages will be in a ratio of 7:6. At the time of their marriage, their ages were in a ratio of 5:4. How many years ago did they marry?
Question
The ages of a man and his wife are in a ratio of 6:5. 6 years from now, their ages will be in a ratio of 7:6. At the time of their marriage, their ages were in a ratio of 5:4. How many years ago did they marry?
Solution
Let's denote the current ages of the man and his wife as 6x and 5x respectively.
According to the problem, 6 years from now, their ages will be in a ratio of 7:6. This gives us the equation:
(6x + 6) / (5x + 6) = 7 / 6
Solving this equation, we get x = 6.
So, the man is currently 36 years old and the woman is 30 years old.
At the time of their marriage, their ages were in a ratio of 5:4. Let's denote the number of years ago they got married as y.
This gives us the equations:
36 - y = 5k (where k is a constant representing the ratio at the time of their marriage)
30 - y = 4k
Solving these equations, we get y = 6.
So, they got married 6 years ago.
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