Final answer:
After deducting one-fifth of the tickets for the ball toss and half of the remaining for the ring toss, then adding the 5 tickets won, Sam has 21 tickets remaining.
Step-by-step explanation:
The student's question involves a series of mathematical operations including subtraction, division, and addition to find out how many tickets Sam has left after playing two games at the carnival. However, the original text of the question is incomplete as it does not specify how many tickets Sam used in the ball toss game. Assuming he used one-fifth of his tickets, as might be implied, we can proceed with the solution.
Initially, Sam has 40 tickets. If he uses one-fifth for the ball toss game, he uses 8 tickets (because 40 divided by 5 equals 8). After this game, he has 32 tickets remaining (40 minus 8 equals 32). Sam then uses half of these tickets on the ring toss game. Half of 32 is 16, so he uses 16 tickets on the ring toss game. After playing ring toss, he is left with 16 tickets (32 minus 16 equals 16). Because he wins 5 more tickets from the game his final count is 21 tickets (16 plus 5 equals 21).
Through these steps, we have calculated that after playing these two games, Sam will have 21 tickets remaining for other carnival games or future use.