The Prince William School Board last week approved a nearly $164.3 million budget for 1987 that would boost salaries of school employes by 5 percent and allow the administration to hire 113 more teachers.

According to school spokeswoman Kristy Larson, the budget is a 14.4 percent increase over this year, most of which will go for pay raises and new teachers to accommodate the 1,300 new students expected next year. The county school system, the third largest in Virginia with nearly 37,000 students, is experiencing soaring enrollment in the midst of Prince William's continuing development boom. The new budget will also bring the salaries for beginning teachers from $17,000 to $19,000, ranking it among the top 10 of Virginia school systems.

Larson said the budget does not include the originally proposed $25 million the School Board said it needs for three new schools because the Board of Supervisors asked that the School Board look at the issue again and come back to it with recommendations. The School Board is slated to meet this week to discuss the proposal to replace Bennett and Saunders elementary schools and Marstellar middle school.

The budget also provides a reserve fund to pay for an additional 25 teachers if enrollment projections prove too low. Last fall school officials scurried to hire teachers after the start of the school year when opening day produced 600 more students than planners had predicted.

Other major new areas of spending in this year's budget, Larson said, are for school maintenance, which has always lost in the past when officials had to set priorities, and for insurance costs, which are skyrocketing.

The school budget will be incorporated into the county budget and then approved by the Board of Supervisors.