A little over a month after voters from RSU 22 member towns of Hampden, Newburgh, Winterport and Frankfort rejected their proposed education budget at the polls, school officials are hoping that the new version they developed strikes a winning balance.

Voters will be asked to approve the new budget during the district budget meeting at 7 p.m. on Tuesday at the Hampden Academy gym.

After hearing from residents who either want to see more money put into instruction or a lighter local share, the school board has taken steps to do both, Superintendent Rick Lyons said Thursday.

“It’s a sound budget. It’s a reasonable increase,” he said.

The new version of the proposed $30,972,944 school budget for this school year reflects a 2.96 percent increase from last year, as opposed to the 2.8 percent increase it called for in the initial version, Lyson said.

That is because RSU 22 received $450,658 more in state subsidy than it anticipated when the school officials adopted the earlier version of the budget, Lyons said.

To that end, the school board proposes using 60 percent of that money to ease the burden on taxpayers in Hampden, Winterport, Newburgh and Frankfort, who would have had to shell out a combined $11,241,060 — almost 4.4 percent more than last year — had the original budget passed.

Instead, they are being asked to contribute $10,936,937, or 1.57 percent more than last year, Lyons said.

Under that scenario, Hampden’s share would be go from the initially proposed $6,546,873, or 3.77 percent over last year, to $6,370,594, or .98 percent up from last year, budget documents posted on RSU 22’s website show.

Newburgh’s share would drop from $1,101,741, up 4.1 percent, to $1,071,632, up 1.26 percent; Winterport’s share would drop from $2,738,615, up 5.92 from last year, to $2,663,836, up 3 percent; and Frankfort’s portion would go from the initially proposed $853,830, up 4.7 percent, to $830,874, up 1.57 percent from last year.

The remaining 40 percent of the additional state aid would be applied to instruction.

While many voters who attended the first district budget meeting spoke in favor of restoring a part-time art position and a full-time English language arts position at Hampden Academy, school officials said the projected enrollment for the coming school year did not justify that.

School officials instead decided to move the art position to the kindergarten and grade one levels, which haven’t had art instruction in at least a decade, Lyons said.

Other positions added for the coming school year include a reinstated half-time kindergarten to grade 8 technology integrator, a teacher sabbatical, a raise from $70 to $75 a day for substitute teachers, additional funds for teaching supplies and $6,000 for the second referendums.

The final step in the budget approval process comes on Tuesday, Aug. 1, when budget validation referendums are held in each of the district’s four member towns. The polls will be open from 8 a.m. to 8 p.m. at the Hampden Municipal Building, Newburgh Elementary School, Samuel L. Wagner Middle School in Winterport and Frankfort Elementary School.