Dollar General said Monday it offered $78.50 a share in cash, or about $8.95 billion, to buy rival Family Dollar Stores Inc., topping Dollar Tree Inc.’s offer for the company three weeks ago.

Shares of Dollar General jumped 11% to $63.90 in recent premarket trading.

The combination of the two discount chains would have about 20,000 stores in 46 states, with sales of more than $28 billion, Dollar General said.

“For Family Dollar shareholders, our proposal is financially superior to the curren

Dollar General

Dollar Tree is buying rival discounter Family Dollar for $8.5 billion, significantly broadening its reach as it looks to fend off Wal-Mart, which has been stepping up its courtship of lower-income customers.

The deal makes Dollar Tree the biggest player in the dollar store segment, with its more than 13,000 combined locations eclipsing current leader Goodlettsville-based Dollar General Corp., which has about 11,300.

Analysts had hinted for months that Dollar General might make