A few years ago, Tressalyn Carson and her three children were living in a motel in Brighton. Between working as an infant-toddler teacher and struggling to find a place to stay, living in temporary housing was a huge burden on Carson and her family. “Every day was uncertain because I had no idea where we would have a home,” she said. “When we were living in the motel, I wasn’t even able to cook meals for my kids.”

Last year, Carson was able to secure an apartment in Dorchester through a subsidy from the Homelessness Prevention and Rapid Re-Housing Program (HPRP), made possible by The American Recovery and Reinvestment Act of 2009. Now out of homelessness, her family has enough space to live and she has been able to pursue a degree.

Carson’s story is an example of the many obstacles lower-income families face in meeting the demands of the state’s rental market. The basis of this was explored in a study published this month by the UMass Boston Center for Social Policy in conjunction with six other agencies. The findings were presented last Thursday at UMass.

The study focused on the experiences of 486 families living in shelters and motels in four regions that receive help through short and long-term subsidies. Through the US Department of Housing and Urban Development (HUD), the state allocated $8.3 million to re-house families. The report ties the lack of market rent affordability to a widening gap in income. With Boston one of the highest-priced rental markets in the country, a family would need 30 percent of a monthly income of $2,960 to $4,497 to afford the fair market price of a two-bedroom unit, according to the study.

One of the authors of the study, Tim Davis, a senior research fellow at the Center for Social Policy, explained that this is why the role of housing agencies to mediate between landlords and offer financial assistance is so integral to impacted families. “Few can afford to find housing in the short term and are forced to double up with families,” he said.

Massachusetts is the only state that provides services to any family experiencing homelessness that qualifies for assistance. But in the years since the economic downturn, the number of people living in poverty has increased by 14 percent statewide. Because there is no cap on the number of families that can be served, the Emergency Assistance program has resorted to putting more and more people up in motels.

The study noted that placing high numbers of families in shelters and motels puts a big financial burden on the state; housing families in apartments is, overall, a better alternative, and comes in at about a third of the cost.

“These types of programs save money in the long-run and they’re also more compassionate,” Davis said.

By the end of the study, the number of families residing in temporary housing was reduced by half. Researchers recommended that some form of a rental subsidy has to be provided for longer periods of time in order to maintain stable housing conditions.

The Center for Social Policy was instrumental in working with legislators to secure $20 million for affordable housing needs. Chris Norris, Executive Director of the Metropolitan Boston Housing Partnership, said that the support of elected officials like state Sen. Sonia Chang-Diaz has helped greatly helped, but there is more hard work ahead.