The Arlington County and Alexandria city governments, divided over how best to pay for a streetcar line through the congested corridor between Pentagon City and Potomac Yards, have crafted a compromise aimed funding the project and addressing the expected growth and density in the area.

The plan, scheduled to be approved by both the County Board and City Council in separate sessions Saturday, calls for Arlington to pay for the streetcar line through an add-on commercial transportation tax, tax-increment financing, bonds and state money, as well as separate federal funds.

Alexandria, which has committed most of its transportation funds to the project, would need $30 million to $100 million worth of federal New Starts and Small Starts funds to build a line if it decides a streetcar is a better option than buses or trolleys.

The compromise became necessary after Alexandria officials became alarmed early this spring when they learned that Arlington decided not to apply for federal funds for the project.

After rumors of a rift between the governments circulated, Alexandria Mayor William D. Euille (D) and Arlington County Board chair Mary H. Hynes (D) talked and agreed to jointly meet with their staffs to work out a solution.

“Rather than competing, we decided to cooperate,” said Euille, who added that there’s a long history of coordination between the neighboring governments and that elected officials and staff from each area regularly meet.

Hynes agreed, noting that the county and city have different challenges. Crystal City is in its second generation of development, while Alexandria’s Potomac Yards is just being built. Despite the differences, Alexandria and Arlington agree that working together on mass transit is critical, she said.

“It’s not an optional choice,” Hynes said. About 5 percent of all traffic in Northern Virginia is on Metro or buses and, she said, “as we continue to add population, if we don’t keep that percentage or grow it, the whole region will shut down.”

Arlington will continue to plan for a streetcar to run from Pentagon City to the border with Alexandria. The city will focus on building a Potomac Yard Metrorail station and decide later whether to apply for federal funds to extend the streetcar line or choose a bus or trolley connection.

Arlington officials have been far more enthusiastic about streetcars than have Alexandria officials. Hundreds of people showed up at two hearings last week to consider and express opinions on whether to build a streetcar line down Columbia Pike between Fairfax County and the Pentagon or whether a less-expensive “bendable” bus was the better option.

Alexandria’s council unanimously agreed Wednesday to launch a free trolley between the King Street Metro station and the Del Ray and Arlandria neighborhoods so residents and tourists can try it out. It will operate on a weekend schedule starting in November. They are also in the midst of plans for several high-capacity corridors across the city and are evaluating whether that would include streetcars or amped-up bus lines.