Marriott Corp. yesterday agreed to sell off one of its marginal businesses - automatic food vending machine services in the metropolitan Washington area, which account for about $4 million of the billion-dollar corporation's annual sales volume.

Wometco Enterprises, Inc., a Miami-based entertinment, bottling and vending firm, agreed to buy the operation for a still-undisclosed amount of cash.

The Miami firm, one of the larger vending machine operators in the southeastern states, has been reported close to an agreement with Marriott earlier this week.

Wometco has extensive vending operations here, with an annual volume of some $3 million from general vending and an additional $6 million in cigaret, music and game machine operations. Senior vice president Bill Welder heads Wometco's area division, based in Cheverly.

Marriott's vending business was confined to Maryland, Virginia and the District of Columbia.

According to Van Myers, senior vice president of Wometco, Marriott officials decided to drop vending "because they believe it was a business they didn't thoroughly understand."

Myers said, in a telephoen interview, that his firm plans to continue employment for about 100 persons who have worked in the Marriott division, which included eight separate vending routes.

"Our business will integrate very nicely with the business they have," he added. Nationwide, Wometco vending sales last year were about $60 million compared with $53 million in 1976. Overall, Wometco revenues in 1976 were $202 million.