Who brought the Centurion's request to Jesus?

Matthew 8:5-13 and Luke 7:2-101

It clearly states that the Centurion came to Jesus in Matt. 8:5. But it also says that the Jewish elders came to Jesus. The order of events seem to be that the Centurion first sent the Jewish elders (Luke 7:3). Jesus then agreed to go. Then the Centurion came to Jesus (Matt. 8:5). Jesus walked everywhere he went. Centurions commanded hundred-men groups in the Roman legion. "Such men were prestigious members of a relatively small class governing the military."2 Therefore, the centurion most probably had a horse upon which to ride to and from where Jesus was. If this is so, then he probably returned to his home, checked on the servant, and then sent friends (Luke 7:6) to speak to Jesus and say that he, the Centurion, was not worthy for Jesus to even enter his home. Jesus continued on. Then as Jesus neared the home, the Centurion himself approached Jesus (Matt. 8:8) to tell Him that he was not worthy for Him to enter his house.

Event	Matthew 8:5-13	Luke 7:2-10
The slave is sick		2 And a certain centurion’s slave, who was highly regarded by him, was sick and about to die.
Jewish elders entreat Jesus		3 And when he heard about Jesus, he sent some Jewish elders asking Him to come and save the life of his slave. 4 And when they had come to Jesus, they earnestly entreated Him, saying, "He is worthy for You to grant this to him; 5 for he loves our nation, and it was he who built us our synagogue."
Centurion approaches Jesus	5 And when He had entered Capernaum, a centurion came to Him, entreating Him, 6 and saying, "Lord, my servant is lying paralyzed at home, suffering great pain."
Jesus goes	7 And He *said to him, "I will come and heal him."
Centurion sent friends to Jesus		6 Now Jesus started on His way with them; and when He was already not far from the house, the centurion sent friends, saying to Him, "Lord, do not trouble Yourself further, for I am not worthy for You to come under my roof; 7 for this reason I did not even consider myself worthy to come to You, but just say the word, and my servant will be healed.
Centurion says he is not worthy	8 But the centurion answered and said, "Lord, I am not worthy for You to come under my roof, but just say the word, and my servant will be healed.
the Centurion speaks of authority	9 "For I, too, am a man under authority, with soldiers under me; and I say to this one, ‘Go!’ and he goes, and to another, ‘Come!’ and he comes, and to my slave, ‘Do this!’ and he does it."	8 "For I, too, am a man under authority, with soldiers under me; and I say to this one, ‘Go!’ and he goes; and to another, ‘Come!’ and he comes; and to my slave, ‘Do this!’ and he does it."
Jesus' words and the servant is healed.	10 Now when Jesus heard this, He marveled, and said to those who were following, "Truly I say to you, I have not found such great faith with anyone in Israel. 11 And I say to you, that many shall come from east and west, and recline at the table with Abraham, and Isaac, and Jacob, in the kingdom of heaven; 12 but the sons of the kingdom shall be cast out into the outer darkness; in that place there shall be weeping and gnashing of teeth." 13 And Jesus said to the centurion, "Go your way; let it be done to you as you have believed." And the servant was healed that very hour."	9 Now when Jesus heard this, He marveled at him, and turned and said to the multitude that was following Him, "I say to you, not even in Israel have I found such great faith." 10 And when those who had been sent returned to the house, they found the slave in good health.