TRYING TO ENTICE MORE PEOPLE to ride commuter rail on the weekends, the MBTA’s oversight board on Monday approved a new $10 weekend pass that entitles the holder to take unlimited trips on the system on Saturdays and Sundays this summer.

The pass is the second part of a first-of-its-kind effort to build ridership on the commuter rail system, particularly on lines that are underutilized. The T and its commuter rail operator Keolis Commuter Services launched a $200,000 advertising campaign in April to build general awareness of the commuter rail system among people traveling into Boston for sporting and other events as well as people who might be reverse commuting from Boston to outlying areas.

Evan Rowe, the T’s director of revenue, said the $10 pass would be available from June 9 through September 2 and allow the holder to bring along up to two children ages 11 or younger for free.

The commuter rail system currently caters to people riding into and out of Boston for work. On weekends, there are fewer trains and those that do run often carry few riders. Rowe said the T currently handles 16,600 passenger trips on Saturdays and 9,000 on Sundays, representing about 5 to 10 percent of weekday ridership. The new campaign is designed to see whether passengers could be convinced to use existing commuter rail trains on weekends by lowering the price of travel.

Rowe said he could envision people in Boston hopping on trains to visit Lowell, Worcester, or Providence, or points in between. He said people outside of Boston could take advantage of the fare to spend the day in Boston and avoid the cost of parking. He noted the $10 pass would save the rider money if he or she takes just one roundtrip; savings would increase dramatically if the pass is used for more trips. A roundtrip between Boston’s South Station and Worcester or Providence costs $23, while a roundtrip between North Station and Lowell costs $20.

The Fiscal and Management Control Board, which approved the $10 weekend pass, also began exploring whether the way the T prices regular commuter rail service makes sense. The T currently charges customers based on travel between zones, but there has been grumbling about the way the zones are configured.

For example, South Station and North Station are in zone 1A. Most zone 1 destinations are at least six miles away and roundtrips between the two zones cost $12.50. But due to the configuration of Boston (North Station is more to the north of the city while South Station is more centrally located) some trips out of South Station to other areas of Boston cost the same as trips from North Station to suburban communities. A roundtrip between North Station and Winchester, for example, costs the same ($12.50) as a roundtrip between South Station and Roslindale Village, West Roxbury of Hyde Park. A roundtrip between South Station and Readville costs $13.50.

Boston City Councilor Michelle Wu has advocated for trips between Boston’s commuter rail stations and South Station to be priced like subway fares, or $4.50 for a roundtrip.

Laurel Paget-Seekins, the T’s head of research, said the current zone system has other anomalies as well. She said the Boston Landing station is in zone 1A but attracts riders from Boston as well as further out on the Worcester Line. She said riders coming to Boston Landing from South Station pay the equivalent of subway fares ($4.50 roundtrip), while someone traveling to Boston Landing from Auburndale in Newton would pay $13.50 roundtrip.