The Arlington County Board yesterday adopted a $211.7 million budget that will cost the average homeowner $22 in higher real estate tax bills while slightly lowering the tax on automobiles and other personal property.

The final budget--up 4.6 percent over last year--provides Arlington schools with the $48.5 million they had requested and a 5 percent cost-of-living pay raise to 3,900 county and school employees.

The board's Democratic minority tried unsuccessfully to prevent the 2 percent reduction in the county's personal property rate, saying the $266,000 being returned to taxpayers was needed to fund capital projects. But the three Republican board members prevailed and on a unanimous vote lowered the personal property tax rate by 10 cents to $5.10 per $100 valuation--the second drop in the rate in a month.

The increase in real estate taxes--from 96 to 98 cents per $100 valuation--marks the first time the Arlington tax rate has gone up since the Republicans took control in 1978. Republican board chairman Stephen Detwiler's support of the 2-cent increase assured its inclusion in the budget.

The board yesterday voted to raise the fee for residential garbage collections from $6.68 to $9.60 per quarter and the residential disposal fee from $7.42 to $8.58 per quarter. The cost of commercial garbage collections will go up from $19 a ton to $21.60.

As a result of this and other revenue increases, the board was able to spend $4.4 million more than the $207 million Acting County Manager Anthony Griffin had proposed several months ago and to save eight of the 22 jobs he had targeted for elimination.

The board yesterday approved an amendment offered by board member Walter Frankland to freeze temporarily the salaries of the county's three highest paid officials now earning at least $61,000. The freeze will stay in effect until after Arlington hires a new manager--a position with an advertised salary of around $65,000.

The board split on partisan lines over a number of issues yesterday--including a Democratic proposal to restore $10,000 in county funds at the Fort Barnard Community Center, a neighborhood recreation facility in a black neighborhood. The plan to restore Fort Barnard's funding failed but Detwiler told neighborhood leaders that the board would listen to proposals to transfer responsibility for the facility to a community group.

Also included in the final budget was $450,000 to repair a leaky roof at the Thomas Jefferson Community Center and School; $250,000 for landscaping in Rosslyn; and $71,000 to prevent hefty fee increases at the county's popular Extended Day Care program, which supervises children at the schools until their working parents are able to pick them up.

The board also set aside a $1 million contingency account as a hedge against a further downslide in the economy and the possiblity of more cuts in federal programs. Arlington last year lost more than $3 million in federal revenues as a result of Reagan administration budget cuts.

Without the 2-cent increase in the real estate tax rate, Detwiler and the Democrats argued, the county would not have been able to meet its responsibilities in these and other programs. Republican board member Frankland yesterday criticized the board's additions to the budget. "I don't think we are doing a very illustrious job in supporting the manager's frugal budget," he said.