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Math Help - Where is logic flaw?

  1. #1
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    Where is logic flaw?

    Hi guys

    Here is the question:

    Jenny has 228 more marbles than jack. if bob gave each of them 133 marbles, she will have twice as many marbles as jack. How many marbles does jenny have?


    I said (jn = jenny, jk = jack):

    jn = jk+228
    jn +133 = 2*jk

    substitute jn-228 for jk in the 2nd equation:
    jn +133= 2*(jn-228)

    solve for jn:
    jn=323

    BUT why does this not work - it seems like it should???

    jn = jk+228

    Add 133 to jenny and jack:
    jn +133= (jk+133)+228 = 2jk

    jn+133 = jk+361 = 2jk

    => jk+361 =2jk
    => jk=361

    so jn +133 = 361+228
    and jn = 456

    Help......please!
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by B_Miner View Post
    Hi guys

    Here is the question:

    Jenny has 228 more marbles than jack. if bob gave each of them 133 marbles, she will have twice as many marbles as jack. How many marbles does jenny have?


    I said (jn = jenny, jk = jack):

    jn = jk+228
    jn +133 = 2*jk

    substitute jn-228 for jk in the 2nd equation:
    jn +133= 2*(jn-228)

    solve for jn:
    jn=323

    BUT why does this not work - it seems like it should???

    jn = jk+228

    Add 133 to jenny and jack:
    jn +133= (jk+133)+228 = 2jk

    jn+133 = jk+361 = 2jk

    => jk+361 =2jk
    => jk=361

    so jn +133 = 361+228
    and jn = 456

    Help......please!
    Let J_n and J_k represent Jenny and Jack respectively.

    Jenny has 228 marbles more than Jack ==> J_n=228+J_k.

    Bob gives them each 133 more -> Jenny now has twice as many marbles as Jack ==> J_n+133=361+J_k=2J_k

    Thus, it follows that 361+J_k=2J_k\implies J_k=361

    Therefore, J_n+133=2\left(361\right)\implies J_n=722-133=589

    Thus, Jenny has 589 marbles and Jack has 361 marbles.

    Does this make sense?
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  3. #3
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    Hi Chris-

    The answer is 323 though (the first way I did it).

    The second way I did it (and you did it) we both got jack = 361.
    But depending on the substitution we made, we got different answers (both wrong).

    Now I am really confused
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  4. #4
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    Quote Originally Posted by Chris L T521 View Post
    Thus, Jenny has 589 marbles and Jack has 361 marbles.

    Does this make sense?
    But that cannot be correct, because Jenny is now supposed to have twice as many marbles as Jack, but 361 * 2 = 722, which does not equal 589.
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  5. #5
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    Quote Originally Posted by B_Miner View Post
    Hi Chris-

    The answer is 323 though (the first way I did it).

    The second way I did it (and you did it) we both got jack = 361.
    But depending on the substitution we made, we got different answers (both wrong).

    Now I am really confused
    When I solved this, I got these values:

    Jack had 95, Jenny had 323 (before bob gave them marbles). After bob gave them each 133, Jack has 228 and Jenny has 456.


    Let x = # of marbles JACK has to start. Then, x + 228 equals the number of marbles JENNY has to start.

    Each of these quantities increases by the same amount, 133, and after this, JENNY has twice as many marbles as JACK. So,

    JACK's marbles JENNY's marbles
    2 * (x + 133) = (x + 228 + 133)

    Jenny's marbles are twice that of Jack's.

    2x + 266 = x + 361
    -x -266 = -x - 266

    x = 95

    This was the number of marbles JACK had to START, remember? So Jenny had 95 + 228 = 323. But remember, BOB gave them each 133 more marbles.

    So
    Jack has 95 + 133 = 228
    Jenny has 323 + 133 = 456
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by B_Miner View Post
    [snip]

    Hi guys

    Here is the question:

    Jenny has 228 more marbles than jack. if bob gave each of them 133 marbles, she will have twice as many marbles as jack. How many marbles does jenny have?


    I said (jn = jenny, jk = jack):

    jn = jk+228
    jn +133 = 2*jk

    substitute jn-228 for jk in the 2nd equation:
    jn +133= 2*(jn-228)

    solve for jn:
    jn=323

    [/snip]

    If you solve for J_n in that equation, you get J_n=589, since

    J_n+133=2\left(J_n-228\right)\implies J_n+133=2J_n-456\implies 133+456=589=J_n...

    Quote Originally Posted by B_Miner View Post
    Hi Chris-

    The answer is 323 though (the first way I did it).

    The second way I did it (and you did it) we both got jack = 361.
    But depending on the substitution we made, we got different answers (both wrong).
    Hm...

    Now I am really confused
    I'm starting to get there...
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  7. #7
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    x = jenny original amount ........ (x - 228) = jack's original amount

    each receive 133 from bob

    x+133 = new amount for jenny ........ (x-228)+133 = x - 95 = jack's new amount

    jenny now has twice what jack has ...

    x+133 = 2(x - 95)

    x+133 = 2x - 190

    x = 323 , jenny's original amount ....... jack's original amount = 323-228 = 95

    both receive 133 ...

    323+133 = 456 ........ 95+133 = 228

    456 = 2(228)
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  8. #8
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    Quote Originally Posted by skeeter View Post
    x = jenny original amount ........ (x - 228) = jack's original amount

    each receive 133 from bob

    x+133 = new amount for jenny ........ (x-228)+133 = x - 95 = jack's new amount

    jenny now has twice what jack has ...

    x+133 = 2(x - 95)

    x+133 = 2x - 190

    x = 323 , jenny's original amount ....... jack's original amount = 323-228 = 95

    both receive 133 ...

    323+133 = 456 ........ 95+133 = 228

    456 = 2(228)
    Hey, that's what I said.
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  9. #9
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    Thanks everyone!!

    I was starting to loose my marbles!
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  10. #10
    Super Member Matt Westwood's Avatar
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    This is what you originally had:

    Quote Originally Posted by B_Miner View Post

    I said (jn = jenny, jk = jack):

    jn = jk+228
    jn +133 = 2*jk
    ... but what you should have started with was:

    jn = jk+228
    jn +133 = 2*(jk + 133)

    ... because after bob gave them BOTH 133 marbles, etc.
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