After dozens of teachers, parents and children told the Prince William Board of County Supervisors about crowded classrooms and outdated sports fields, the supervisors voted to advertise a compromise tax rate lower than the community members had asked for, but higher than the county executive’s original proposal for the fiscal 2015 budget.

Again and again, community members told the board at a lengthy meeting Tuesday night: Advertise the current tax rate.

Only at the current rate of $1.18 per $100 of assessed value, those advocates said, would the county have the money to reduce class sizes, pay more to teachers and county employees, add lights and other amenities to sports fields, hire more police officers and firefighters, improve public transportation, and support a variety of social service organizations.

Keeping the tax rate at the current year’s level would not mean keeping residents’ tax bills the same. Because property assessments in the county have gone up, the same tax rate would lead to a 7.5 percent increase in the average residential tax bill.

In her $975 million budget, proposed the week before Tuesday’s meeting, County Executive Melissa S. Peacor proposed a much lower tax rate of $1.12 per $100 of assessed value. That rate would spell a 2.5 percent increase in the average residential tax bill.

Supervisors voted to meet in the middle, agreeing on an advertised rate of $1.158 per $100 of assessed value.

The advertised rate will not necessarily be the actual tax rate when the board finalizes the budget next month. After Tuesday, supervisors can set a lower rate but not a higher one. That means the average residential bill will not increase by more than 5.4 percent.

Before the board voted on the rate, dozens of residents expressed their willingness to pay higher taxes to fund improved county services. Four community members used the comment period to ask for lower taxes or to criticize the board’s previous financial management. About 60 adults and three children asked that the board advertise the current rate or an even higher one, or spoke about specific services that need more funding.

“We have done the austerity thing. We’ve done it better than most. And we are at a point where cutting just won’t cut it,” said Sheyna Burt, chairman of the Prince William County Arts Council. Burt was one of many who said that the county should stop budgeting as though it were in a recession.

The most commonly mentioned problem was class sizes in the public schools. Teachers spoke of classes with up to 37 students in which science experiments are not safe, students are noisy and instructors can barely move between desks.

One first-grade teacher said she teaches 26 children in a room where more than 20 desks cannot fit comfortably. “It is really like being in an overcrowded elevator all day long,” she said. “Most adults hate being put on hold for a phone call. Try being a little 6-year-old and having to wait and wait and wait for the teacher to help you. Very frustrating and sad. I often feel the children in my class are put on hold.”

Prince William has the largest class sizes in Virginia. But school officials said that even with a tax increase, they can make only modest strides toward addressing the problem.

They estimated that removing just one child from each class in the county would cost $15 million. Instead, Milton C. Johns (At Large), chairman of the School Board, asked for funding for a $3.9 million plan, which he said would reduce class sizes in kindergarten, most sixth-grade subjects and ninth-grade math.

Speakers at the meeting asked for money in the budget to hire police and fire personnel, to improve the county’s bus system and to support local nonprofit groups. The condition of sports fields was also frequently mentioned.

Jeremy Sachs held his 6-year-old son, Chase, up to the microphone so Chase could say: “Me and my team, we would like lights for when we play late games at night.”

The public comment period lasted three hours, and the board began its discussion about 10:30 p.m. The first motion, to advertise the current rate as residents had prodded, won the votes of four out of eight supervisors. To pass, a motion needs five votes.

Corey A. Stewart (R-At Large), chairman of the Board of Supervisors, was among those who voted for the highest rate. “We started a cost-cutting austerity program in this county,” he said. “We did kick the can down the road on a lot of services we knew we needed to get back to when the recession started lightening up.”

Stewart insisted that the board would not ultimately pass a budget with a tax increase anywhere near the $1.18 rate but said that an advertised rate of $1.16 — meaning an average tax increase of more than 5.5 percent — would be too tight to give the board room to craft its final budget.

Eventually, the board pushed even lower than that, setting a rate of $1.158, with only Frank J. Principi (D-Woodbridge), who supported rates between $1.167 and the current rate, opposed.