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Math Help - Word problem (my teacher is crazy)

  1. #1
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    Word problem (my teacher is crazy)

    The following is a well known children's rhyme.

    As i was going to St Ives,
    I met a man with seven wives;
    Every wife had seven sacks;
    Every sack had seven cats;
    Every cat had seven kits;
    Kits,cats, sacks, and wives,
    How many were going to St Ives?

    Often people answer "one" as the rhyme never indicates that anyone else is actually going to St Ives. However, assuming that the entire group is actually going to St Ives show that the answer to the question is in the rhyme sum of a geometric series, and finds its sum.
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  2. #2
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    Quote Originally Posted by gumi View Post
    The following is a well known children's rhyme.

    As i was going to St Ives,
    I met a man with seven wives;
    Every wife had seven sacks;
    Every sack had seven cats;
    Every cat had seven kits;
    Kits,cats, sacks, and wives,
    How many were going to St Ives?

    Often people answer "one" as the rhyme never indicates that anyone else is actually going to St Ives. However, assuming that the entire group is actually going to St Ives show that the answer to the question is in the rhyme sum of a geometric series, and finds its sum.
    r = 7, a = 1

    s5 = (1(1-7^5))/(1-7) = 2801

    Plus the man narrating makes it 2802.
    Last edited by sean.1986; May 30th 2008 at 01:51 PM.
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  3. #3
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    Hello, gumi!

    As I was going to St Ives,
    I met a man with seven wives;
    Every wife had seven sacks;
    Every sack had seven cats;
    Every cat had seven kits;
    Kits, cats, sacks, and wives,
    How many were going to St Ives?

    Assuming that the entire group is actually going to St Ives,
    show that the answer to the question is the sum of a geometric series, and finds its sum.
    Let's count the items . . .

    I met a man with seven wives . . . 1\text{ man, }7\text{ wives}
    Every wife had seven sacks . . . 7^2\text{ sacks}
    Every sack had seven cats . . . 7^3\text{ cats}
    Every cat had seven kits . . . 7^4\text{ kits}


    Then: . S \;= \;1 + 7 + 7^2 + 7^3 + 7^4 \;=\;2801

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  4. #4
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    Quote Originally Posted by Soroban View Post
    Hello, gumi!

    Let's count the items . . .

    I met a man with seven wives . . . 1\text{ man, }7\text{ wives}
    Every wife had seven sacks . . . 7^2\text{ sacks}
    Every sack had seven cats . . . 7^3\text{ cats}
    Every cat had seven kits . . . 7^4\text{ kits}


    Then: . S \;= \;1 + 7 + 7^2 + 7^3 + 7^4 \;=\;2801

    Wrong. You forgot to include the man who met the man with 7 wives.
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