Blake plays football. Last year, he averaged 280 passing yards per game during his team’s 9-game season. The school record for total passing yards in a season is 3, 114 yards. If Blake increases his passing yards per game by 25% this year, how close will he come to breaking the record?
a)he will break the record by 36 yards b)he will break the record by 29 yards c)he will be 369 yards close to breaking the record d) he will be 531 yards short to breaking the record
The Correct Answer and Explanation is :
To solve this problem, let’s calculate Blake’s projected passing yards for the current season based on a 25% increase in his average passing yards per game.
- Calculate last year’s average passing yards per game:
Blake averaged 280 passing yards per game over 9 games. Therefore, his total passing yards for last year was:
[
280 \, \text{yards/game} \times 9 \, \text{games} = 2,520 \, \text{yards}
] - Calculate the new average passing yards per game:
If Blake increases his passing yards per game by 25%, his new average would be:
[
280 \, \text{yards/game} \times 1.25 = 350 \, \text{yards/game}
] - Calculate the projected total for the current season:
With a new average of 350 yards per game over the same 9-game season:
[
350 \, \text{yards/game} \times 9 \, \text{games} = 3,150 \, \text{yards}
] - Compare with the record:
The school record for total passing yards in a season is 3,114 yards. We find the difference between Blake’s projected passing yards and the record:
[
3,150 \, \text{yards} – 3,114 \, \text{yards} = 36 \, \text{yards}
]
So, if Blake achieves a 25% increase in his passing yards per game, he will break the record by 36 yards.
Explanation
The correct answer is (a) he will break the record by 36 yards. This is determined by calculating both his new average passing yards per game and his projected total for the season. By increasing his passing rate by 25%, Blake surpasses the previous record, indicating that even a relatively modest improvement in performance can yield significant results over multiple games.