Question: A person has three types of juice, $A$,$B$,$C$ costing $18$ coins per ltr, $25$ coins per ltr and $36$ coins per ltr. In what ration does he have to mix the three juices so that selling the entire mix at $23.10$ coins per bottle, he can make a profit of $10\% ?$
Let us assume that he sells $x$ ltr of $A$, $y$ ltr of $B$ and $z$ ltr of $C$. Then $A:B:C=x:y:z.$ Then $$(x+y+z)\times {2310\over 100}={110\over 100}\times \left(18x+25y+36z\right)\\ \implies231\times (x+y+z)=11\times(18 x + 25 y + 36 z)\\\implies 3 x-4 y-15 z=0$$ Now,from this one equation, how can one find the values of $3$ variables $x,y,z$? Should the question have more information? Pardon me if this is too easy to be asked here.
Thank you.