Celebrating Agebra with my friend

Algebra Level 3

I was in a party with my friend Ashish and we both were holding a glass containing alcohol and water in some ratio. The glass that I was holding contained the ratio as \(4:1\)(alcohol:water). And the glass that Ashish was holding contained ratio as \(9:1\)(Alcohol:water). Now, I poured both of our mixtures in a bigger glass which can hold the mixtures from both the glasses. If the resulting mixture has alcohol and water in the ratio \(x:y\) where \(x\) and \y) are co-prime positive integers. Then find the value of \(x+y\).

It is known that the glasses that we were holding were of same volume. And both of them were filled up to the rim.


This problem is a part of the set All-Zebra

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