Fairfax County Board of Supervisors Chairman Sharon Bulova (D). (Michael S. Williamson/WASHINGTON POST)

The Fairfax County Board of Supervisors is leaning toward adopting a 2017 budget that would raise property taxes for homeowners by an average of $304 per year and use most of the new revenue to fund county schools.

In a proposal county supervisors reviewed Friday, the nation’s 10th-largest school system would get an extra $88.4 million next year, an acknowledgment of warnings from school officials that repeated shortfalls in funding have led to larger class sizes and an exodus of frustrated teachers that places Fairfax schools in jeopardy.

The proposal, which the county board is scheduled to vote on later this month, comes as Virginia’s largest municipality struggles to maintain its infrastructure and vaunted services in a weak economy that has not kept pace with the demands of a population that is growing older and poorer.

“This process is never easy, but it’s the most important thing that we do throughout the entire year,” board Chairman Sharon Bulova (D) said during a budget committee meeting Friday. “When you adopt a budget, you are investing in the community’s priorities. That is not an easy thing to do, and striking the right balance is critical.”

A 4-cent increase would raise the county’s residential tax rate to $1.13 per $100 of assessed value — an amount anti-tax groups have argued will be too burdensome for lower-income homeowners in one of the country’s most expensive regions.

To offset those concerns, county supervisors made plans to renew discussions about asking Fairfax voters to approve a tax on restaurant meals. The board also will explore the possibility of levying taxes on cigarettes or alcohol purchased in the county. And it plans to investigate how to provide more tax relief to low-income seniors.

For now, the budget proposal cooled tensions over funding between county supervisors and school officials while still promising county employees raises of at least 3.3 percent next year and setting aside $2.4 million for police department reforms and $3.9 million to increase services for residents with mental health problems.

School officials said the proposal significantly reduces what began as a $67.8 million funding shortfall in their $2.67 billion budget. After adding in some newly allocated state funding, the shortfall is now about $15.7 million, officials said.

Superintendent Karen Garza said her staff could work with that amount, a reaction that also showed in the smiles of several county School Board members who attended the budget committee meeting.

“The increase in county funding provides us the opportunity to make a significant and critical investment in employee compensation, and reducing class size, while not cutting vital student programming,” Garza said in an emailed statement. “We are hopeful that this is reflective of a turning point in our community.”

Whether that holds true depends on how well the local economy performs.

For the 2018 budget year, county budget officials are projecting a shortfall of $75 million, based on the health of the local real estate market and other factors.

“That is a real number that we will have to pay attention to next year,” said Supervisor Jeff C. ­McKay (D-Lee), who chairs the budget committee and crafted much of the proposal.

The proposal includes recommendations for better cooperation between elected officials in the school system and county government, including a joint retreat in June.

“Next year will be another tough year,” McKay said, adding that many residents have expressed deep concerns about whether the county would again raise taxes. “We need to be extraordinarily mindful of that as our two boards collaborate.”