A single mother's determined journey from welfare to work earned her a trip to the White House to see President Reagan sign legislation designed to help other women do the same.

"I'm a happy person now that I'm working and I'm not on welfare," said Evelyn Vega, 28, of Stamford, Conn. "Now that the government did all this, it could be a chance to help a lot of women like me."Reagan signed a major welfare overhaul bill Thursday that will offer education, training and work programs aimed at putting welfare recipients to work. Vega, whose trip to Washington was funded by the United Way, said she considers herself a symbol of the gains other women can make.

Three years ago Vega was on welfare and could not read or write, much less hold a job.

Now, with help from government and non-profit groups, she manages a fast-food store, has her own car and says her goal is to send her three daughters to college.

Vega, whose parents separated when she was young, said she largely raised herself after running away from home at age 10. She and an older sister traveled from Puerto Rico to several U.S. states, and Vega became pregnant for the first time at age 15.

Three years ago, when all of her daughters were old enough to attend school, Vega went to her welfare caseworker and said she wanted to get off public assistance.

"I was so lonely. I was so scared," she said. "I didn't want to sit there with my girls going to school and me doing nothing."

Vega got a tutor, Page Oristano, from the Literacy Volunteers of America, who began to teach her reading, writing and basic skills such as how to look up a number in the telephone book.

Eventually another non-profit group agreed to help her find an entry-level job in a fast-food store, and the manager there decided to help her train for a management job.

She passed the management test a month ago with 98 of 100 possible points. Several months earlier, Vega received her last welfare check.

"I'm a single woman and I'm just taking care of my girls and I'm happy," Vega said. "Sometimes I feel like I'm drowning, but it's OK."

She reads at the third or fourth grade level, but higher when the material is job-related, and she has a good chance of finishing high school, Oristano said.

Vega's goal is to send her daughters to college, get her high school diploma and eventually attend college herself.

Vega said she is convinced other welfare mothers can get off public assistance.

"They've got to say, `I'm going to do it. I'm going to stick with it and I'm not going to go back,"' she said.

The Family Support Act signed by Reagan on Thursday provides money to states and requires them to offer education and job training to women with children age 3 and over. It also puts new pressure on absent parents to pay child support.

The incentive to get off welfare," Vegas said, "has to come from the person because the programs are there."