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Story highlights

Arizona Sen. John McCain faced a Republican primary challenge from Kelli Ward

Democratic Rep. Debbie Wasserman Schultz faced Tim Canova in Florida

(CNN) —  

The incumbents won the night in several highly watched races Tuesday night. CNN projected Republican Sens. Marco Rubio of Florida and John McCain of Arizona and Democratic Rep. Debbie Wasserman Schultz of Florida all won their primary races Tuesday night.

Nightcap: The latest news and political buzz from CNN Politics | Sign up

Rubio, a first-term senator, faced off against wealthy businessman Carlos Beruff – while on the Democratic side, Rep. Patrick Murphy defeated Rep. Alan Grayson and will take on Rubio in November.

Wasserman Schultz bested her Bernie Sanders-backed rival.

And McCain faced a test from Kelli Ward, a conservative 33 years McCain’s junior who had suggested his age (he turned 80 on Monday) means he’s too old for a sixth term.

Going into the night, four incumbents had already lost this year – with Republican Reps. Renee Ellmers of North Carolina, Randy Forbes of Virginia and Tim Huelskamp of Kansas and indicted Democratic Rep. Chaka Fattah going down in primaries.

Arizona Senate race

McCain had a clear lead of 55% to 29% over Ward in a CNN/ORC poll of likely voters two weeks ago – with a margin of error of plus or minus 5 percentage points.

But even years after his choice of Sarah Palin as his 2008 presidential running mate helped inspire the tea party movement, McCain still must defend his conservative credibility against a hardline opponent.

And his party’s presidential nominee, Donald Trump, has called McCain – a Navy veteran and prisoner of war in Vietnam – weak on veterans’ issues.

Ward, a physician, has used McCain’s 80th birthday to call him “old” and “weak” in national interviews.

“John McCain has stayed in Washington, D.C., for way too long – almost four decades,” she told CNN’s Brooke Baldwin last week, saying that McCain and his own family members had reservations about his age. “The Arizona voters will decide if they want an 80-year-old senator or not.”

Ward hit the same theme Monday in an interview with CNN’s Wolf Blitzer, saying: “I do want to give him the best 80th birthday present ever: the gift of retirement.”

Wasserman Schultz’s test

Already on thin ice with her party’s left wing – mostly Sanders supporters who believed she favored Hillary Clinton in the primary – Wasserman Schultz was imperiled when the Wikileaks hack of Democratic National Committee emails became public.

But she was able to defeat her opponent nonetheless, despite her difficulties.

Ex-DNC chair, Sanders-backed challenger face off Tuesday

She was forced to announce her planned resignation on the eve of the Democratic convention in Philadelphia, suffering a major public embarrassment a little more than a month before her primary.

Sanders lent his mailing list to Canova, though he didn’t campaign with him in the weeks preceding the primary there.

“We’ve really got so much grassroots energy coming our way right now. The momentum is all on our side,” Canova told CNN’s Wolf Blitzer in a Monday interview.

Florida Senate primaries

Since Rubio reversed his decision to retire, he and Murphy, the Democratic congressman, have been largely focused on each other – each expecting to sail through primaries.

Ahead of Florida primary, Rubio offers Trump a tepid embrace

Beruff spent $7 million of his own money, but never closed the gap with Rubio.

Grayson, meanwhile, had a hard time winning over voters amid reports he abused his ex-wife. He was also badly outraised by Murphy.