The Arlington County Board has decided it does want the school board to aim for a $47.5 million budget next year, even if that figure results in a cut in programs.

The county board's 3-to-2 vote yesterday was supposed to clarify goals for school spending next year but even the Republican majority admitted that the school board is unlikely to follow its instructions to the letter.

"The school board has never been able to live within guidelines," said board member Walter Frankland. "There's something about guidelines that sends them into orbit."

Indeed, Torill B. Floyd, the school board's lone Democrat who last week threatened to resign over the issue of budget guidelines, said yesterday she expects the board will present the county with "different options" fluctuating around the $47.5 million figure.

"I don't think we can come in at $47.5 million unless we again cut services," said Floyd after the county board vote. "I believe with declining enrollment we can cut administrative staff some, but not to the tune of $2 million. We can't cut that much."

School administrators have told the board that to maintain programs, Arlington schools would need $46.8 million in fiscal 1983, not including any cost-of-living raise for teachers and other employes. The estimated cost to the schools of a 5 percent across-the-board salary increase, the figure now contemplated for other county employes, is $2.5 million.

Although the 1983 budget is still months away from a vote, the county board, apprehensive about further federal cuts and a slowdown in construction and property value increases, has tried at least to set some parameters on spending. However, the budget debate so far has caused more confusion, which has been heightened by the partisan split on the board.

Yesterday, Democrats insisted that the $47.5 million school budget and the $158 million overall county budget should be considered as a "floor," to be used to set priorities for county programs. Democrat John Milliken described the figures as the first step in a "budget preparation exercise," a view rejected by the board's three Republicans.

To Frankland, it is already an issue of taxes versus services. "We've overlooked the fact that these figures have a built-in 10 percent tax increase" resulting from an increase in property assessments, said Frankland. He warned that any spending over $158 million next year will require an actual increase in the tax rate.