Question 805678
Wrong equation.
The amount of juice is {{{0.7*30=21}}} quarts (70% of 30 quarts) in the undiluted juice.
That plus {{{0}}} quarts of juice in the added water has to add to the amount of juice in the final dilution, which should be {{{0.6*(30+w)}}} quarts of juice
The equation is
{{{0.6(30+w)=0+0.7*30}}}
{{{18+0.6w=21}}}
{{{0.6W=21-18}}}
{{{0.6w=3}}}
{{{w=3/0.6}}}
{{{highlight(w=5)}}} quarts.
 
The mistake:
Using 100, 70 and 60 for 100%, 70% and 60% means that the quantities in your equation are not in quarts, but in fancy units of your invention.
That makes it difficult to relate equations with the "real" situation, but we could work with that, if we prefer large numbers to decimals.
However, if we accept your units,
{{{60(30+w)}}} represents the amount of juice in {{{30+w}}} quarts of final diluted mixture,
{{{2100=(70)(30)}}} represents the amount of pure, undiluted juice in the initial {{{30}}} quarts of original "juice (drink) that is 70% juice".
However, adding to that {{{2100}}} a {{{100w}}} term makes no sense.
Maybe {{{100w}}} could represent the amount of water in the {{{w}}} quarts of 100% pure water added, but it does not make sense to add the initial amount of pure juice plus the initial amount of pure water to find the final amount of pure juice.
It would make more sense to add {{{0w}}}, representing the amount of juice in the {{{w}}} quarts of pure water (containing 0% juice) added.