Prince William County police still have no suspects and no motive and are "perplexed" in their investigation of the execution-style murders of three young women in Dale City on Saturday, a police spokesman said yesterday.

The three women were each shot once in the back of the head and found lying side by side in a trailer used as a housing development office. Police yesterday called the shootings the worst crime in the history of the county.

The three were not sexually molested before they were shot with a small caliber weapon between 4 and 6:55 p.m. on Saturday, according to an autopsy, part of which was made public by police yesterday.

Police said about $30 in cash was taken from the three women's purses, along with other personal items that police would not identify. There were no signs of a struggle in the trailer and robbery did not appear to be a major motive for the slaying, police said.

Sharon Lake, 25, of Dale City, and her friend, Debra Warner Frank, 23, of Alexandria, were found dead in the trailer they had gone to as part of an afternoon of house hunting for Frank. Also found in the trailer, which sits near the end of a dead-end road and is bordered by excavated land soon to be a housing development, was Karen Rose Scarbrough, 17.

Police said Scrabrough, who graduated from high school a week before her death, was working the first day of her first job when she was shot. She died on the way to Potomac Hospital in Woodbridge, police said.

The trailer, which was closed for business yesterday, is a sales office for Ryland Homes, the developer clearing land nearby. Police said Ryland's sales manager John McCauley found the bodies at 6:55 p.m. when he went inside the trailer to use the phone.

"This is a complicated case," Officer Ted McInteer, the spokesman, said yesterday. "Who travels the dead-end of Dale Boulevard?"

Police said they are searching for possible witnesses who were riding Saturday afternoon in a red Volkswagon with Maryland license plates, looking for houses in Dale City, a sprawling development of about 30,000 located 30 miles south of Washington. Police described the driver of the car as a white male about 45 years old. Three young women (not the murder victims) were riding with him, police said.

No neighbors, according to police, heard shooting inside the trailer. Police said they found an air conditioner running at the murder scene, and they speculated yesterday the gunshots may have been muffled inside the trailer so as not to be audible from the nearest house about 75 yards away.

Sharon Lake, who with her husband had recently purchased a house in Dale City about a mile from where her body was found, was to have taught her last day of the spring school term yesterday at Occuquan Elementary School in Woodbridge.

Instead, her substitute sat down with Lake's class of first graders and talked with them about why people murder each other.

"Most of the people in the world are good, but a few of them are bad," the children concluded, according to Betty Erickson, the substitute. She said some of the 6-and 7-year-olds in the class mistakenly called her "Mrs. Lake" yesterday. Other children immediately corrected them, according to Erickson, saying, "Mrs. Lake is in Heaven."

Lake moved to the Washington area from Louisiana where she had been teaching, according to Occoquan Elementary principal Richard Gastley. He described Lake as an "execeptional first-grade teacher" who devoted herself to both the children and their parents.

The husbands of Lake and Frank are friends who both work at the Pentagon in the Air Force Data Services Center. Capt. Calvin K. Lake is a computer program analyst, according to an Air Force spokesman. Sandy Frank is a civilian mathematician.

According to a neighbor who lives next door to the Lake's home, Lake left the Washington area yesterday for his wife's funeral in Canton, Ohio, her home town.

Deborah Frank worked for a government consulting firm in McLean where she did a variety of jobs, ranging from compiling reports to handling interoffice communications, according to a spokesman for the BDM Corp.

She did not handle classified government documents, which might possibly have provided a motive for her murder, according to the spokesman.

Frank, who moved to the Washington area in 1977 soon after she married, will be buried today in a suburb of Bufflao, the spokesman said.