Question 972934
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You didn't bother to include a value for the sum their ages, so I will assume that the sum is some constant *[tex \Large S].  Then let the man's age be represented by *[tex \Large x_m] and the woman's age be represented by *[tex \Large x_w].  Hence we have:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_m\ +\ x_w\ =\ S]


and since the man was the woman's age the difference between their two ages years ago, we can write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_m\ =\ 2\left(x_w\ -\ (x_m\ -\ x_w)\right)]


First simplify the second equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_m\ =\ 2\left(2x_w\ -\ x_m\right)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3x_m\ =\ 4x_w]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_w\ =\ \frac{3}{4}x_m]


Then substitute into the first equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_m\ +\ \frac{3}{4}x_m\ =\ S]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_m\ =\ \frac{4}{7}S]


And therefore


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x_w\ =\ \frac{3}{7}S]


Once you figure out what S really is, you can do the arithmetic and come up with hard numbers.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \