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  • A Math Proportion Quiz Question

    Anonymous Christian
    Sep 5, 2014
    MATH, Math Olympiad
    Comments Off on A Math Proportion Quiz Question

    Question

    If a hen and a half can lay an egg and a half in a day and a half, how many eggs can six hens lay in seven days?

     

    Answer

    Just write the sentences and you will get the answer!?

    1.5 hen lays 1.5 eggs in 1.5 day

    Now think.

    Now four ” 1.5 hen ” [ that is 1.5*4 = 6 hens ] will lay four sets of “1.5 eggs” [ that is 1.5*4 = 6 eggs ] in just 1.5 day!!!

    So, 6 hens lay 6 eggs in 1.5 day

    In four “1.5 days” [ that is 1.5*4 = 6days], 6 hens would have laid a total of 4*6 = 24 eggs.

    That is, 6 hens lay 24 eggs in 6 days

    For the seventh day, it actually depends on what you assume proportional to what. Its a matter of interpretation and assumption. 3 possiblities only for assumption of proportionality, and each is given below.

    Note : In each of the below, we will use the fact
    “6 hens lay 24 eggs in 6 days” because it was
    derived independent of any other extra assumptions.

    Interpretation 1.(eggs are laid in proportional to the days discretely)
    Using 6 hens lay 24 eggs in 6 days.
    Now, In 6 days, 6 hens can lay 24 eggs. What about one day?
    In one day, 6 hens can lay 4 eggs by assuming the eggs are layed in proportional to the days… i.e, 4 eggs per day from this statement. Thus in the seventh day, 4 eggs are produced by 6 hens. Hence total eggs = 24 + 4 = 28 eggs.

    Interpretation 2.(eggs are proportional to the hen discretely)
    If we assume the eggs are proportional to the hen.
    then, from 6 hens lay 24 eggs in 6 days.
    Then, 1 hen lays 4 eggs in 6 days. By further assumption that eggs and hen are proportional continously we get : one hen lays (7/6)*4 eggs in (7/6)*6 = 7 days;
    Total eggs = 6* (7/6)*4 = 28 eggs.

    Interpretation 3 ( hen is proportional to the days discretely )
    This makes no sense, since the number of hens is NOT proportional to the days.

    Both “possible” ways indicate the answer is total 28 eggs (Answer).

    P/S:

    If you see carefully, actually, interpretation 1 and 2 are the same because we cannot escape the fact that the eggs are laid out proportional to the hens!

     

anonymous-christian

Jonathan Ramachandran is founder at AnonymousChristian.org which serves as a Christian Blog discussing the Greater Hope of Biblical Christian in Christ Alone. He is also an IMO (International Math Coach) and a featuring Guitarist for many bands.

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