The 112 sixth-grade students and their families sitting in the sweltering auditorium had never before seen the blond woman at the podium. Yet she was promising to change their lives.

"I am here to give you a present," she said. "An offer none of you can refuse, I promise you. "

Then Diane Weiss, the wife of a wealthy Connecticut stockbroker - a man who worked his way through the University of Pennsylvania - stunned the Belmont Elementary School's Class of 1987.

"You have won the lottery," she said. " . . . How can you collect? The payoff is a college education. I'm here this morning to tell each and every one here that we will guarantee your college education. My family will pay for every bit of it. "

For the children and their families - most of them poor, many of them single parents on welfare who never got through high school themselves - the import of Weiss's words took a second or two to sink in.

Overwhelmed, teachers started to cry before many of the parents seemed to catch on.

"That means," Weiss repeated, her voice quivering with excitement, "if each and every youngster on this stage graduates from high school with a diploma and is accepted at college or a technical-training school, we'll pay all costs of tuition. "

"Everything," she affirmed.

There was a collective gasp. Then many parents and teachers in the auditorium stood and cheered. The students themselves, at first perplexed, started clapping too.

Diane Weiss beamed. The offer came from Weiss and her husband, George, a self-made Hartford, Conn., multimillionaire who financed his education at Penn's Wharton School with loans and summer jobs. Weiss had been hospitalized suddenly with a bad back and was forbidden by his doctors from attending yesterday's announcement.

Eager to repay Penn and its West Philadelphia neigborhood, Weiss, 44, had approached his alma mater with a lot of money and a desire to make a meaningful contribution. The Collaborative for West Philadelphia Public Schools, a coalition of educational institutions and local businesses chaired by Penn President Sheldon Hackney, jumped into action.

It suggested a program modeled after one begun by New York philanthropist Eugene Lang. During a graduation ceremony at his old elementary school in East

Harlem six years ago, Lang impulsively promised to pay for the college educations of all 57 graduates - if they could make it through high school.

With two-thirds of those students graduating from high school this year, Lang has expanded the program to other cities through the I Have a Dream Foundation, inspiring other philanthropists - most recently in Washington and Los Angeles - to make similar offers.

Penn officials consulted with School Superintendent Constance E. Clayton and her advisers in choosing Belmont, at 41st and Brown Streets, in the heart of impoverished West Philadelphia. The school's entire student body is black and two-thirds of the students' families receive welfare.

Citywide, almost 40 percent of all students drop out before finishing high school, but the rate for students coming from neighborhoods like Belmont's is much higher, according to district officials.

Norman Newberg, an education professor at Penn who specializes in disadvantaged students, estimated that in a class such as Belmont's, maybe 10 percent of the students would go on to college without the kind of support and incentive the Weisses are providing.

The Weisses also plan to hire a tutor-counselor to help the students choose careers, select courses in high school, deal with family problems and avoid the lure of the streets. Diane Weiss said her family, including her two teenage daughters, would get personally involved in the children's lives over the next six years.

"Obviously this is not something for nothing," Weiss told the students. ''You need to put in effort, and so should we. . . . Remember the deal, you graduate from high school and we will pay the cost of college tuition. You must graduate.

"We believe you should have a chance to push yourselves to the highest level that you can and possibly beyond," she continued. "And we believe that not having enough money to do that should not be an issue. "

Before they learned of their fortune, the students had addressed the pitfalls they face. All seven students speaking at the graduation ceremony warned of the lure of drugs. "To achieve our goals we must get a good education," said Lamont Goings in his speech. "We must not use drugs or alcohol. "

Students and their families came to yesterday's ceremonies expecting some kind of surprise. The television lights and the presence of Clayton, Board of Education President Herman Mattleman and dignitaries from the University of Pennsylvania heightened the suspense.

Principal Sophie Hayward had hinted in a letter earlier in the week that ''history would be made. "

"Some students told me they thought the President was coming," Hayward said. "Or the mayor. One teacher said Stevie Wonder. But my response to everybody was that it was something much, much better than all of these things. "

After the ceremony, Vera Billups, 26, held her 1-year-old son and talked about her oldest son, Majovie, 12. "This will make a lot of difference," she said. "I'm proud he's going to get the opportunity to go to college. "

Billups said she dropped out of school at 14 when she was pregnant with Majovie. Her brother, Ernest Bland, said he, too, left school early, to go to work. "We'll make sure he stays on his feet and makes no bad turns," Bland said of his nephew.

"I was totally astonished," said Patricia Ollivierre , whose son, Jarmain, wants to be an astronaut. "I'll push for him to finish his education. "

"A lot of these kids have the potential but not the finances to go to

college," said Marcia Green, their fifth-grade teacher. "Now they know if they continue to try, there is hope at the end. Without this, they might give up. "

Hayward has been credited by parents, teachers and Clayton with working wonders at the school. A buoyant woman with seemingly unlimited faith in her students, she said she believes all the students will benefit from the Weisses' offer - even the third or so of the class now classified as learning disabled.

"My feeling about it is that Einstein was in special classes and look where he wound up," said Hayward.

Added Clayton: "It's just the most extraordinary opportunity for boys and girls in this school to understand how important they are. Now they know that not just their parents and their teachers, but other people believe in them as people with potential."