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“It seemed like there were a lot more cheers in the audience for [Kentucky Sen.] Rand Paul than there were for John McCain, who I think represents the old party,” she said. “We’re the future of the Republican Party.”

The only two living former presidents who are Republicans, George W. Bush and George H.W. Bush, were relegated to video appearances during the convention. With his approval ratings reaching historic lows in August 2008, George W. Bush also addressed that year’s convention via video after weather nixed the first day’s events in St. Paul, Minn.

“Our generation has to step aside for the younger generation, and when you see people like [Susana] Martinez and Paul Ryan, you think, ‘Oh, there is hope,’” said Mary Vickers of Hernando County, Fla.

Ms. Vickers and Maureen Arrigale, who was accompanying her, were a bit cagey when asked for their ages, but both made it clear they were seniors who were nevertheless ready to embrace Mr. Ryan.

“I’m the senior that Obama claims Ryan is throwing off the cliff,” Ms. Arrigale quipped.