If Metro's 100-mile system is to be completed, Arlington County must come up with about $57 million in constructions costs. Operating costs the country will have to pay for the bus-rail system will be about $9 million next year and escalate to $20.2 million by 1990 if fares are increased by half the rate of inflation.

Those figures were released last week at a meeting o the Arlington County Board by Metro Board Chairman Joseph S. Wholey, who is also a member of the Arlington Board. Wholey's presentation was the first in a series of sales pitchs to local governments of Metro's proposed financial plan. Local jurisdictions such as Arlington [WORD ILLEGIBLE] then, in the era of Proposition 13, decide how to pay for their share of the system.

In releasing the financial plan last month, Wholey warned that if any jurisdiction refuses to pay its share of Metro, "the system would grind to a halt."

U.S. Transportation Secretary Brock Adams has said that the Carter Administration is committed to the goal of completing the 100-mile system, but local governments must first guarantee payment of construction and long-term operating costs.

The financial plan envisions an 80-20 split, with the federal government picking up 80 percent of the cost of the system and state and local jurisdictions splitting the remainder. Cost of completing the full system, now projected for 1967, is close to $3.2 billion.

According to Wholey, Arlington's share of construction costs could be financed through a bond issue.

Operating costs, which must be paid through a combination of fares and local tax revenues, represents one of the thorniest political issues in selling the plan. A bill proposing a one-cent sales tax, which would cover an estimated $1.2 million of Arlington's debt service over the next 30 years, as well as operating subsidies was defeated by one vote in the last session of the General Assembly.

Even if the bill had passed, Virginia Governor John Dalton is known to be unenthusiastic about the prospect of a special transit tax and has said he might have vetoed it.

"The simple solution," quipped Arlington Board Chairman John W. Purdy at one point in Wholey's presentation, "is to get this all embodied in the Defense Department budget."

The Arlington Board is scheduled to consider ways of financing the system, including a possible bond of referendum, on Oct. 14.