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Question Number 194888 by Abdullahrussell last updated on 18/Jul/23

	Answered by aleks041103 last updated on 18/Jul/23

	$T h e c o m b i n e d a g e s o f M a r y a n d A n n i s 44 y e a r s .$ $(M (t_{1}) + A (t_{1}) = 44)$ $M a r y i s t w i c e a s o l d a s A n n w a s$ $(M (t_{1}) = 2 A (t_{2}))$ $w h e n M a r y w a s h a l f a s o l d a s A n n w i l l b e$ $(M (t_{2}) = \frac{1}{2} A (t_{3}))$ $w h e n A n n i s t h r e e t i m e s a s o l d a s M a r y w a s$ $(A (t_{3}) = 3 M (t_{4}))$ $w h e n M a r y w a s t h r e e t i m e s a s o l d a s A n n .$ $(M (t_{4}) = 3 A (t_{4}))$ $A l s o w e k n o w t h a t M - A = c o n s t .$ $l e t A (t_{4}) = x$ $\Rightarrow M (t_{4}) = 3 x \Rightarrow M - A = 2 x$ $\Rightarrow A (t_{3}) = 3 M (t_{4}) = 3.3 x = 9 x$ $\Rightarrow M (t_{2}) = \frac{1}{2} A (t_{3}) = \frac{9}{2} x$ $\Rightarrow A (t_{2}) = M (t_{2}) - 2 x = \frac{5}{2} x$ $\Rightarrow M (t_{1}) = 2 A (t_{2}) = 5 x$ $\Rightarrow A (t_{1}) = M (t_{1}) - 2 x = 5 x - 2 x = 3 x$ $\Rightarrow M (t_{1}) + A (t_{1}) = 5 x + 3 x = 8 x = 44$ $\Rightarrow x = \frac{11}{2}$ $\Rightarrow M (t_{1}) = 5 x = \frac{55}{2} = 27.5$ $\Rightarrow M a r y i s 27 a n d a h a l f y e a r s o l d .$
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