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  1. #1
    Silver Lounger
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    Numbers Everywhere!

    1. <LI>Find two different whole numbers such that neither number contains any zeros and their product yields 1000000000.
      <LI>Four different whole numbers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, multiply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the four original numbers that sum to 125?

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  3. #2
    Star Lounger
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    Re: Numbers Everywhere!

    a. <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">512 * 1953125</span hide>
    b. <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">1,5,24,96</span hide>

  4. #3
    Star Lounger
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    Re: Numbers Everywhere!

    b. oops! <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">-2,2,25,100</span hide> <img src=/S/blush.gif border=0 alt=blush width=15 height=15>

  5. #4
    Star Lounger
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    Re: Numbers Everywhere!

    b. <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">3, 7, 23, 92</span hide>

  6. #5
    Platinum Lounger
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    Re: Numbers Everywhere!

    a) Just to give you the full set and the only one answer:

    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">
    1 1000000000
    2 500000000
    4 250000000
    5 200000000
    8 125000000
    10 100000000
    16 62500000
    20 50000000
    25 40000000
    32 31250000
    40 25000000
    50 20000000
    64 15625000
    80 12500000
    100 10000000
    125 8000000
    128 7812500
    160 6250000
    200 5000000
    250 4000000
    256 3906250
    320 3125000
    400 2500000
    500 2000000
    512 1953125
    625 1600000
    640 1562500
    800 1250000
    1000 1000000
    1250 800000
    1280 781250
    1600 625000
    2000 500000
    2500 400000
    2560 390625
    3125 320000
    3200 312500
    4000 250000
    5000 200000
    6250 160000
    6400 156250
    8000 125000
    10000 100000
    12500 80000
    12800 78125
    15625 64000
    16000 62500
    20000 50000
    25000 40000
    31250 32000
    32000 31250
    40000 25000
    50000 20000
    62500 16000
    64000 15625
    78125 12800
    80000 12500
    100000 10000
    125000 8000
    156250 6400
    160000 6250
    200000 5000
    250000 4000
    312500 3200
    320000 3125
    390625 2560
    400000 2500
    500000 2000
    625000 1600
    781250 1280
    800000 1250
    1000000 1000
    1250000 800
    1562500 640
    1600000 625
    [b]<big>1953125 512 <---------------THIS ONE</big>[b]
    2000000 500
    2500000 400
    3125000 320
    3906250 256
    4000000 250
    5000000 200
    6250000 160
    7812500 128
    8000000 125
    10000000 100
    12500000 80
    15625000 64
    20000000 50
    25000000 40
    31250000 32
    40000000 25
    50000000 20
    62500000 16
    100000000 10
    125000000 8
    200000000 5
    250000000 4
    500000000 2</span hide>
    Jerry

  7. #6
    Silver Lounger
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    Re: Numbers Everywhere!

    Several stabs were taken at the ([img]/forums/images/smilies/cool.gif[/img] puzzle and so far, all are incorrect. I'll post the correct solution in a day or two if no one solves it.

  8. #7
    Star Lounger
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    Re: Numbers Everywhere!

    Now you do have me stumped.

    "Four different whole numbers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, multiply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the four original numbers that sum to 125?"

    1st number : 3
    2nd number: 7
    3rd number: 23
    4th number: 92

    3+7+23+92=125

    1st number increased by 4: 7
    2nd number decreased by 4: 3
    3rd number multiplied by 4: 92
    4th number divided by 4: 23

    Same numbers as before, only in different order. Still add to 125.

    Actually, there are more solutions: 8,12,21,84; 13,17,19,76; 18,22,17,68. I guess I don't understand the question.

  9. #8
    Plutonium Lounger
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    Re: Solution

    I think the confusion is caused by the word "equivalent". "Equal" would have been more appropriate.

  10. #9
    Platinum Lounger
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    Re: Solution

    I see your point but the term equivalent is correct in the algebraic sense as it means "two or more expressions that have the same value"... just a comment
    Jerry

  11. #10
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    Re: Solution

    Based on your directions shouldn't this be:
    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">16 + 24 + 5 + 80 = 125.</span hide>

    The numbers in yours (since you created the algebraic solution not based on the "order") is in the wrong order:
    "Four different whole numbers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, multiply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the four original numbers that sum to 125"

    Now, when the first is increased by 4, the second is decreased by 4, the third is multiplied by 4 and the fourth is divided by 4 all give you <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">20</span hide>. In your order this does not work out... <img src=/S/smile.gif border=0 alt=smile width=15 height=15>

    Steve

  12. #11
    Silver Lounger
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    Re: Solution

    OK

  13. #12
    Silver Lounger
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    Solution

    Perhaps the wording of the puzzle is a bit confusing. I apologize. The one and only correct solution along with the math behind it is noted below...

    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">The objective is to find four numbers that add to 125 whereby those four numbers become equivalent (the same number) after adding 4 to one, subtracting 4 from another, multiplying one by 4 and dividing the last by 4. If this is more clear than the original instructions, stop here before proceeding to the final solution...</span hide>

    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">The math behind the solution: (x+4) + (x-4) + (4x) + (x/4) = 125
    6x + x/4 = 125
    25x/4 = 125
    x=20</span hide>

    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">In the end, you have: 16 + 24 + 5 + 80 = 125. You can see now, that by adding 4 to one of the numbers, subtracting 4 from another of the numbers..., they all become equivalent (equal to 20).</span hide>

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