why wont my snapper lawn mower keep running after it starts?

I bought a lawn mower (snapper push 5 horse six speed )at a garage sale and I put fresh gas in it.There appeared to be no gas in prior to me doing so and I checked the oil which was fine. I made sure there was no obstructions under the deck ect. then I went to start it. To my delite it popped off right away but after running for about 45 seconds it died and would only start when I pushed the plunger on the carberater to prime. It then would run a little while then die, and this seems to be the pattern! Could you help me. I cant aford to take it in!Any help would greatly be appreciated, thank you for your time ...........Patrick