Judy Campbell, Brennan’s guidance counselor at Hollywood High School, where three of every four students qualify for a free or reduced-price lunch, suggested that his family was “not poor enough for need-based aid and not rich enough to write a check.”

Image Brennan Jackson and his father, Aaron, searched the Internet for scholarships to help pay for Brennans freshman year at the University of California, Berkeley. Credit... Monica Almeida/The New York Times

When asked over dinner whether she felt guilty that Brennan had taken so much upon himself, his mother, Caryn, began to cry. “We didn’t expect to end up in this situation,” she said.

Tuition, board and other expenses at Berkeley are estimated at $27,000 a year. Last year, the family’s income was $58,000, when Ms. Jackson’s wages from teaching were combined with revenue from a part of a rental property. The family cannot sell the property because it does not own it outright, and Ms. Campbell believes that the investment reduced the direct aid Brennan might have received.

Brennan’s father, Aaron, who was laid off as an accountant more than a year ago, acknowledged that his son had few options. He said his lack of steady income prevented the family from refinancing the $500,000 mortgage on its cramped, nearly 90-year-old, two-bedroom home or taking on additional debt.

Mr. Jackson said his job search had been frustrating: he said he had been deemed overqualified for some jobs in recent months, and underqualified for others. His previous job with a real estate company paid about $75,000 annually.

Which is not to say that the family has not been doing its part to offset its expenses.

They have reduced visits to the dentist from twice a year to once; saved $45 a month in groomers’ fees by trimming their two dogs themselves; returned one of their cars, a Honda CRV on a lease, to the dealer; stopped eating in restaurants; and deferred home repairs.