State budget cuts and declines in philanthropy and endowments helped push the cost of college tuition up much higher than general inflation across the country this year, amounting to an increase of 7.9 percent at public campuses and 4.5 percent at private ones, according to a study by the nonprofit College Board.

 Tuition and fees for the current school year average $7,605 for state residents at public four-year colleges and $27,293 at private institutions, according to the report released Thursday. Room and board added an average of $8,535 at public campuses and $9,700 at private schools.

 However, significant boosts in federal grant aid and the use of tax credits provided so much relief that many families, particularly low-income households, were shielded from those price increases, the report found.

 “That doesn’t mean families aren’t struggling to pay. They are struggling to pay,” Sandy Baum, a policy analyst for the College Board, said Thursday. But she noted that “extraordinary increases” in federal Pell grants for low-income students and education benefits for military veterans allowed many to enroll and stay in school even as unemployment rose.

 The average undergraduate last school year received $6,041 in various grants and $4,883 in loans, the study said.

 About 55 percent of recent graduates at public colleges borrowed some of the cost of college and their debt total averaged $19,800, the College Board said. At private nonprofit colleges, 65 percent of graduates borrowed money, and on average owed $26,100.

 With general inflation only 1.2 percent, the cost of college without financial aid sped past other consumer costs as it has for three decades, officials noted. The biggest jump came at state institutions, for which state revenues declined as a result of the recession.

 Public universities that offer doctorates now average $8,503 for tuition and fees, up 8.9 percent from last year, the College Board said. The University of California approved a 32 percent increase rise in basic undergraduate fees for this school year, bringing those well above the average to about $11,300, not including living costs, a figure well above the national average.

 The report showed that state universities that mainly offer bachelor’s and master’s degrees averaged $6,588 in tuition and fees this year, up 6.5 percent. Undergraduates at California State University pay about $5,100, after a 5 percent increase that still kept them below the national average for this year.