Question

A tank of water is `5/9` full of water. If a `6 3/4` liters of water is poured it will be `2/3` full. What is the capacity of the tank?

Answer 1

As the question uses fractions the answer should be in fractions.

The total volume of the tank is `60 3/4" litres"`

`color(blue)("This solution is using algebra but it is in disguise")`

Explanation:

The question is not complete in its description, in that it does not state if the water is removed or added.

The change is `" "5/9 " to "2/3`

which is the same as `" "5/9" to "6/9`

As `6/9` is more than the starting point then it is added.
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The difference is `1/9` as a consequence of adding `6 3/4` litres

So `color(brown)(1/9xx"tank"=6 3/4)` litres

Multiply both sides by `color(blue)( 9)`

`color(brown)(color(blue)(9xx)1/9xx"tank"=color(blue)(9xx)6 3/4)`

`" "1xx"tank"= 9xx27/4" " =" " 60 3/4" litres"`