Jane had a bottle filled with juice. At first, Jane drank 1/5 the 1/4, followed by 1/3. Jane checked how much juice was left in the bottle: there was 2/3 of a cup left. How much juice was in the bottle originally?
Bottle originally had
As Jane first drank
Let us assume there were
Jane first drank
then she drank
and then she drank
each unit must be
Hence bottle originally had
Based on the stated assumption:
I chose the presentation to show the way of thinking when doing algebra.
Consider the denominators. I chose to do it this way:
Convert all the denominators into
Note that 47 is a prime number so this can not be simplified
We need to change the
Multiply both sides of Equation(1) by