Elite colleges can enroll more low-income students…

America’s top colleges are filled with rich kids.

The class divide is deeper than you might have thought. Ivy League colleges, for example, have more students from the top 1% of income than the bottom half.

Meanwhile, tens of thousands of low-income students would qualify to enroll in an elite college but are attending a less selective institution instead, according to a report from Georgetown University’s Center on Education and the Workforce.

These students scored above the median on the SAT or ACT among all students at selective institutions. The report defines low-income students as those who receive Pell Grants from the federal government. The grants are mostly awarded to those whose families earn less than $30,000 a year.

Where you go to college can make a big difference. Students at top colleges are much more likely to graduate, regardless of their family income. And despite the cost of getting a degree, those who do will earn more over their lifetime.

Related: More proof that college is key to the American Dream

The report calls on colleges to enroll more low-income students so that they make up at least 20% of the student body. Most colleges already do this, but there are 346 that fall short.

To meet the 20% threshold, they would have to enroll 72,000 more Pell Grant recipients. That shouldn’t be a problem since there are 86,000 who would qualify, according to the report. (About 39% of all college students receive Pell Grants.)

But it would cost the schools more money because they’d have to offer bigger financial aid awards so that these students could afford to enroll. They’d either have to enroll more students in general, or replace students who would pay closer to the full tuition cost.

“I think it’s an easy ask,” said Anthony Carnevale, the director of the Georgetown University Center on Education and the Workforce.

“These are not-for-profit institutions and, by law, they have to serve a public purpose,” he said.

Almost half of those institutions that currently fall short of the 20% threshold are considered most, highly or very competitive. Many of these colleges have run budget surpluses over the past four years, according to the report. The 69 most selective private colleges that enroll less than 20% Pell Grant recipients each had an average budget surplus of about $139 million, or about 6% of their annual budget.

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A group of the nation’s top colleges has made it a priority to enroll more qualified, low-income students. They’ve formed the American Talent Initiative, which now has 68 members. Presidents at those colleges have pledged to change their recruitment strategy, expand need-based aid programs, and offer support services to make sure these students graduate on time.

Some lawmakers have also paid attention to the issue. Last year, legislation was introduced in the Senate that would require selective colleges to boost the enrollment of low-income students or face paying a penalty.

The bill was introduced by Delaware Senator Christopher Coons, a Democrat, and Senator Johnny Isakson, a Republican from Georgia, but didn’t have further support.

CNNMoney (New York) First published May 2, 2017: 12:01 AM ET