Question 511218
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I don't see where the sum of the ages is very helpful.  You need two variables, one for each person's age.


Let *[tex \Large \alpha_1] represent the child's age and let *[tex \Large \alpha_2] represent the mothers age.


Situation Today:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \alpha_1\,:\,\alpha_2\,::\,3\,:\,5]


Which is to say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\alpha_1}{\alpha_2}\ =\ \frac{3}{5}]


Then you can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \alpha_1\ =\ \frac{3}{5}\alpha_2]


Situation five years hence:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \alpha_1\,+\,5\,:\,\alpha_2\,+\,5\,::\,7\,:\,11]


Which is to say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\alpha_1\,+\,5}{\alpha_2\,+\,5}\ =\ \frac{7}{11}]


Cross-multiply:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 11\alpha_1\ +\ 55\ =\ 7\alpha_2\ +\ 35]


Substitute *[tex \Large \frac{3}{5}\alpha_2] for *[tex \Large \alpha_1] and then solve for *[tex \Large \alpha_2].  Then calculate *[tex \Large \frac{3}{5}\alpha_2] to derive *[tex \Large \alpha_1].


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