Let's break down the yard gains and losses for each of the four plays:
- Play 1: The Tigers gain 6 yards.
- Play 2: The Tigers lose 3 yards.
- Play 3: The Tigers lose 2 yards.
- Play 4: The Tigers gain 7 yards.
To find the total yards gained or lost, we need to sum these values.
Calculate the total yards step-by-step:
1. Start with the first play: 6 yards
2. Add the second play: [tex]\( 6 + (-3) = 3 \)[/tex] yards
3. Add the third play: [tex]\( 3 + (-2) = 1 \)[/tex] yard
4. Add the fourth play: [tex]\( 1 + 7 = 8 \)[/tex] yards
So, the total yards gained by the Tigers over these four plays is 8 yards.
Let's now check the answer choices:
(a) Yes. The team gains more than 10 yards because [tex]\( 6 + 7 + (-3) + 2 = \)[/tex] yards, so the team keeps possession of the ball.
- Calculation: [tex]\( 6 + 7 + (-3) + 2 = 6 + 7 - 3 + 2 = 12 \)[/tex] yards. This is incorrect because the third play should subtract 2, not add 2.
(b) Yes. The team gains more than 10 yards because [tex]\( 6 + 3 + 2 + 7 \)[/tex] is greater than 10 yards, so the team keeps possession of the ball.
- Calculation: [tex]\( 6 + 3 + 2 + 7 = 18 \)[/tex] yards. This is incorrect because we added positive 3 and 2, rather than subtracting them as indicated in the second and third plays.
(c) No. The team gains 8 yards because [tex]\( 6 + (-3) + (-2) + 7 = 6 + (-5) + 7 = \)[/tex].
- Calculation: [tex]\( 6 + (-3) + (-2) + 7 = 6 - 5 + 7 = 1 + 7 = 8 \)[/tex] yards. This matches our detailed calculations.
Thus, the correct interpretation of the plays and the total yardage gained indicates that yes, the Tigers gain 8 yards, which is less than the necessary 10 yards required to retain possession. The correct answer is [tex]\( (c) \)[/tex]: the Tigers gain 8 yards because [tex]\( 6 + (-3) + (-2) + 7 = 8 \)[/tex] yards.
