A container of juice can fill either 35 bottles or 55 cups exactly. The capacity of each bottle is 60 ml more than each cup. What is the capacity of a cup?

1. Formulate an equation based on the total volume of juice

Let the capacity of a cup be $x$ ml.
The capacity of a bottle is $(x + 60)$ ml.
Since the container can fill either 35 bottles or 55 cups exactly, the total volume is the same:
$55x = 35(x + 60)$

2. Solve the equation to find the capacity of a cup

$55x = 35x + 2100$
$55x - 35x = 2100$
$20x = 2100$
$x = \frac{2100}{20} = 105$