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LOUISVILLE, Ky. — Appealing to working parents buckling under financial pressure, Hillary Clinton said on Tuesday that families should not have to pay more than 10 percent of their income on child care.

“If we’re going to say we are for family values, then we need to value families,” Mrs. Clinton said in a speech at a health center while campaigning in Kentucky, whose Democratic primary is next Tuesday.

In Kentucky, Mrs. Clinton said, a family with both parents earning minimum wage has to spend about 20 percent of its income on child care, while a single parent earning the minimum wage has to spend 40 percent of his or her income.

Mrs. Clinton did not spell out how she would ensure that families’ costs would not exceed 10 percent, although her campaign said her plan to limit costs would include subsidies and tax relief.

A report released in October by the Economic Policy Institute, a liberal research group, examined how much of a family’s earnings are consumed by child care costs in 10 metropolitan areas around the country. In those areas, child care costs for an infant and a 4-year-old accounted for roughly 20 to 30 percent of the median family income, the report said.

In her speech, Mrs. Clinton outlined a variety of goals to help reduce the stresses on working parents, including encouraging employers to improve “unpredictable, absolutely backbreaking schedules” for workers and expanding home visiting programs, in which nurses and social workers visit new and expectant parents. She also said she would work to increase the pay of child care workers.

At the same time, Mrs. Clinton took aim at the presumptive Republican nominee, Donald J. Trump, bringing up his stance earlier in the campaign about wages — he said they were “too high,” although he has recently said otherwise — as well as his desire to repeal the Affordable Care Act.

“I think with somebody like Donald Trump, you would see a race to the bottom across our country, with working families paying the price,” Mrs. Clinton said. “And I don’t think that’s a risk we can afford.”

In recent days, Mrs. Clinton’s team has been relentless in branding Mr. Trump as dangerous and divisive, while Mrs. Clinton has focused mostly on issues.

Earlier on Tuesday, she also held a discussion with a small group of parents in Lexington. She spoke of her own time as a mother and grandmother, recalling a lesson she learned after the birth of her granddaughter, Charlotte.

“I never swaddled Chelsea,” she said. “And now it’s like, ‘Oh, you’ve got to swaddle the baby.’ So, learning how you swaddle a baby — you know, that’s an art form.”

