(FORTUNE Magazine) – South Carolina has become the fourth state to subcontract nursing-home care for some of its ailing military veterans. The others: Alabama, Maryland, and Mississippi. More may follow. The number of U.S. veterans age 65 and over has more than doubled to 6.7 million since 1980 and will reach an estimated 8.6 million in the year 2015 as Vietnam-era vets begin to reach retirement age. However, the Department of Veterans Affairs gives those with service-related problems priority for nursing-home care. What about the others? Washington wants the states to help. Congress is likely to increase fiscal 1992's matching-fund program that pays 65% of new nursing-home construction costs, raising it 27% over 1991 to $85 million. Since this program began in 1960, 32 states have built 57 homes for veterans with a total of 12,500 beds. The VA's 126 facilities have 13,000 beds. But the states find the homes expensive to run, even with VA contributions, Medicaid, Medicare, and any private insurance patients may have. South Carolina, for example, built a 220-bed nursing home in Anderson. To operate it would have cost the state an estimated $6.8 million a year, or $85 per vet each day. PHP Healthcare, a public company in Alexandria, Virginia, will now do the job for less than $75, saving the state about $800,000 a year. PHP operates another nursing home for veterans in Alexander City, Alabama. Not every state likes this approach. Says Richard Heuckendorf, veterans' affairs director in Oklahoma, which has six homes with more than 1,100 beds: ''Though it may be economical initially, a private company will keep raising contract prices. By then, it would be too late for the state to get back into the game.''