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William says that if Harry has 8 hits in his next 28 at bats, he will increase his batting average, which is currently 0.308. Charles says that William is wrong. Who is right and why?

How do I figure his current average?

  • Math -

    Forget his current average for a minute.

    Now, what batting average does 8 hits in 28 make? (Divide 8 by 28.)

    We don't know how that .308 was made up, but we know that if 8/28 is greater than .308, he's batting better than his past average, so the average will go up. Equally, if it's less, it will go down.


    Joe hits 4 in ten games, average is .4 = 4/10.
    Now Joe hits 1 in the next 5 games. Average for those 5 is 1/5 = .2, which is lower.
    Now consider his whole average: hit 5 in 15 games = 1/3 = .333, so we can see how the average was lowered by that streak of 5 games.

  • Math -

    8 divided by 28 is .2857. If the current average is .308 then the average would go down not up, right?

  • Math -

    If the current average is .2857 then it would have gone down from .308?

  • Math -

    (Yes I did, but I'm back. Hey, it's Saturday!)

    Yes! Not that the _current_ average is .2857, just that the average of the new games that are added on is .2857.

    If Harry batted exactly .308 in the next 28, his average would stay the same, at .308. If he bats lower, the average will go down. If he bats higher, the average will go up.

  • Math -

    I understand! Thank you for helping me on your Saturday! I am stuck on a similar triangle problem. Sara has been trying to help me. Do you have any input?

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