The Alexandria School Board voted last night to ask the City Council to approve a $45.9 million budget to run the city schools next year.

The total, which includes a 5 percent teacher pay raise and a cut of 27 teaching positions that apparently will require some layoffs, is within the 8 percent budget increase guideline set by city manager Douglas Harman.

The city is being asked to contribute $39.9 million (83 percent) of the proposed school budget.

In its final budget deliberations, the board reinstated several programs that Superintendent Robert W. Peebles had proposed cutting. Yielding to a spirited lobbying effort by high school students, the board reinstated high school football and band camps and new blazers for the school orchestra for a total of $13,596 and decided to save a summer drivers' education program for $19,552. They also increased the school's contingency fund by $30,000 and added $74,970 to the bus transportation fund.

To pay for these additions the board slashed an additional $125,000 from capital outlay, maintenance and equipment-repair portions of the budget and $14,000 from an employe assistance program.

The board voted down several attempts to raise the salaries of board members--currently $125 a month--although the school board chairman was awarded $500 more a year.

The city council is expected to act on the budget in May.