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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?

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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.

This problem has been solved

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