Jim's football team started a play on the 50 yard line. On the first play, the team had a 7-yard gain. On the second play, they lost 10 yards. What yard line was the ball on at the end of the second play?

The team gained 7 yards on the first play, so they advanced to the 50 + 7 = <<50+7=57>>57 yard line.

Then, on the second play, they lost 10 yards, so they moved back to the 57 - 10 = <<57-10=47>>47 yard line. Answer: \boxed{47}.

To determine the yard line at the end of the second play, we need to add the gain from the first play and subtract the loss from the second play.

Starting at the 50 yard line, we have a 7-yard gain on the first play, so we move forward 7 yards.
50 + 7 = 57 yard line.

However, on the second play, the team lost 10 yards, so we need to move backward 10 yards from the current yard line.
57 - 10 = 47 yard line.

Therefore, at the end of the second play, the ball was on the 47 yard line.

To find the yard line where the ball was positioned at the end of the second play, we can start from the initial position on the 50-yard line and adjust it based on the yard gains or losses.

1. The team started on the 50-yard line.
2. On the first play, they had a 7-yard gain, which means they moved forward by 7 yards. So, we add 7 yards to the initial position of the ball.
50 + 7 = 57
The ball is now on the 57-yard line.
3. On the second play, they lost 10 yards, so we subtract 10 yards from the current yard line.
57 - 10 = 47
The ball is now on the 47-yard line.

Therefore, at the end of the second play, the ball was on the 47-yard line.