Question 769883
Let m = mass of the tank by itself (when empty).

Let w = mass of water in FULL tank.


Full tank is {{{m+w=27.5}}} kg.
Quarter-full tank is {{{m+w/4=12.2}}} kg.


Those are two equations using unknown variables m and w.  Various ways possible to solve the system.


{{{m+w/4=12.2 }}},
{{{4(m+w/4)=4(12.2)}}}
{{{4m+w=48.8}}}

{{{(4m+w)-(m+w)=48.8-27.5}}}  which is just subtracting the Full equation from the Quarter-full equation.
{{{3m=21.3}}}
{{{highlight(m=7.1)}}} kg., the empty tank.




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You can continue for finding w.  Either original equation can be used.
{{{m+w=27.5}}}
{{{w=27.5-m}}}
since we found m now,
{{{w=27.5-7.1}}}
{{{highlight(w=20.4)}}} kg. water when full.