Question 278524
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Let *[tex \Large x] represent the mother's age now.  Let *[tex \Large y] represent Jasmine's age now.  Thirty years ago (I'm assuming the "thir" you typed means thirty), the mother was *[tex \Large x\ -\ 30] and Jasmine was *[tex \Large y\ -\ 30].  And we are given that:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ y\ =\ 100]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ 30\ =\ 9\left(y\ -\ 30\right)]


Re-write the second equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -x\ +\ 9y\ =\ 240]


Add the re-written second equation to the first equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ x\ +\ y\ +\ 9y\ =\ 100\ +\ 240]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10y\ =\ 340]


Solve for *[tex \Large y] to find Jasmine's age now.  To check your work, subtract that result from 100 to find the mother's age now.  Then subtract 30 from each of the 'now' ages and verify that the larger is 9 times the smaller.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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