Dr. Johnson and his wife have a combined age of 91.

Dr. Jonson is now twice as old as his wife was when he was as old as she is now.

How old are they?

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Answer:

Dr. Johnson is   52, and his wife is 39.
Let Dr. Johnson’s age be D, and his wife’s age be W. Then we have:
D + W = 91                           (1)
Their age difference is D – W. We know  that Dr. Johnson is 2 x (how old his wife was when he was her age), so we need to take their age difference off his current wife’s age, as follows:
2 x (W – (D – W)) = D
2 x (W – D + W) = D
2 x (2W – D) = D
4W – 2D = D
4W = 3D
W = 3D ÷ 4

Using this in (1) gives:
D + W = 91
D + 3D ÷ 4 = 91
4D + 3D = 364
7D = 364
D = 52
Therefore,  W = 39.

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