As I said, Paul quotes the very words that Jesus spoke during the Last Supper (I Corinthians 11). So he is using some then available source. The Gospels and the various letters can very easily have occurred within the same time frame.Which ones do you think came after the gospel accounts?
Paul’s letters were written sometime between AD 48 to AD 64. They almost certainly predate the Gospels and Acts and so are the earliest existing writings that we have concerning Jesus’ teachings and the doctrinal and organizational development of the early Church.
The majority of scholars hold to a late-dating of the Gospels, placing them in the range of AD 70-100. Since Paul died by AD 67 under the reign of Emperor Nero, we can date his letters from AD 48-67. Therefore, Paul’s writings existed decades before the Gospels existed.
Appealing to the "majority of scholars" doesn't actually hold as much weight as you might think. Scholars are wrong about a great many things. Those scholars you are referring to are usually not Christians at all. The reason why they think the Gospels were written between 70-100AD is because they have to have them after 70 AD and the destruction of the temple. No one could possibly have predicted events in the future - is what they think so it must be after the fact. When actually the Gospels were all written BEFORE 70 AD and very likely well before. The first one probably within 10 years of Messiah's death in 31 AD. And Paul most likely wrote Hebrews anonymously within 15 years (he could not sign his name because it took a while for his past reputation to be forgiven).