# 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?

Oct 3, 2016

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

The total volume of the tank is $60 \frac{3}{4} \text{ litres}$

$\textcolor{b l u e}{\text{This solution is using algebra but it is in disguise}}$

#### 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 $\text{ "5/9 " to } \frac{2}{3}$

which is the same as $\text{ "5/9" to } \frac{6}{9}$

As $\frac{6}{9}$ is more than the starting point then it is added.
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The difference is $\frac{1}{9}$ as a consequence of adding $6 \frac{3}{4}$ litres

So $\textcolor{b r o w n}{\frac{1}{9} \times \text{tank} = 6 \frac{3}{4}}$ litres

Multiply both sides by $\textcolor{b l u e}{9}$

$\textcolor{b r o w n}{\textcolor{b l u e}{9 \times} \frac{1}{9} \times \text{tank} = \textcolor{b l u e}{9 \times} 6 \frac{3}{4}}$

$\text{ "1xx"tank"= 9xx27/4" " =" " 60 3/4" litres}$