Final answer:
The solution of sugar, salt, and vinegar used for making pickles is a hypertonic brine solution that creates osmotic pressure to preserve the cucumbers by dehydrating bacteria.
Step-by-step explanation:
Billy Bob's grandmother is making pickles by putting slices of fresh cucumber into a solution of sugar, salt, and vinegar. This process involves osmotic pressure, where the high concentration of substances in the solution draws out water from the cucumber slices, causing them to shrink.
The type of solution made by this mixture of sugar, salt, and vinegar is a brine solution which is hypertonic relative to the cucumber cells. This hypertonic solution increases the osmotic pressure, dehydrating the bacteria that are not accustomed to such an environment and preventing their growth, thereby preserving the pickles.