Juice and water swapped back and forth

Two glasses hold equal volumes, one of orange juice and one of water. Some water is poured into the juice, then some of the resulting mixture is poured back into the water glass so the volumes are equal again. Let $x$ be the percentage of water in the water glass and $y$ the percentage of juice in the juice glass. Find $x-y$.

0. Each glass ends with volume $V$. Whatever water $w$ sits in the juice glass must be balanced by exactly $w$ of juice in the water glass, so both glasses are $(V-w)/V$ pure. The two percentages coincide.