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?

See the answer

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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