It was recently estimated that homes without children outnumber homes with children by about seven to five. If there are 2556 homes in a county, how many of them are homes without children?

929

Step-by-step explanation:

For every 11 children, 7 will have homes and 4 will not.

The fraction of children without homes is 4/11.

The number of children without homes is

4/11 * 2556 = 929

Check:

The number of children with homes is 2556 - 929 = 1627

With/Without = 1627/929 = 7.005/4 ≈ 7/4

OK.