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?

1 Answer
Tony B
Oct 3, 2016

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.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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"#

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