WASHINGTON — Gov. Jay Inslee on Thursday said Washington will increase monthly heating assistance for low-income families to get around a new federal rule that threatened $70 million in annual food-stamp benefits.

Washington joins seven other states that have already tweaked the so-called “heat and eat” formula in response to a Republican-authored provision in the 2014 farm bill that more closely tied food-stamp allotments to a household’s utility expenses.

Until recently, the federal government provided automatic, $1-a-year heating assistance to all families receiving food stamps, officially called Supplemental Nutrition Assistance Program (SNAP). That allowed families to claim standard deductions for utility costs, which lowered their household income for calculating SNAP benefits. But that shortcut credited some people, such as those whose rent included utilities, with expenses they didn’t incur.

House Republicans rewrote the farm bill to close what they called a loophole. Now, states must provide more than $20 a year in aid from the Low-Income Home Energy Assistance Program before food-stamp beneficiaries can claim the utility deductions.

Inslee said Washington will do just that. Washington was one of 13 states and the District of Columbia that had been using the “heat and eat” maneuver. Oregon, Pennsylvania, New York, Connecticut, Rhode Island, Montana and Vermont have taken similar steps.

Without the change, Inslee said, 200,000 Washington households faced cuts to food-stamp allotments. The state will now ask all SNAP applicants for proof of utility payments. Those without separate utility bills will automatically be given $20 in heating aid.

“Obviously, the loss of tens of millions of dollars aimed at feeding hungry families is not acceptable,” Inslee said in a statement.

About 1.1 million Washington residents receive food stamps, called Basic Food. Forty percent are children and 10 percent are seniors. Benefits average about $125 a month per person.

Kyung Song: 202-383-6108 or ksong@seattletimes.com. Twitter: @KyungMSong