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Math Help - Problem solving formula - results don't match

  1. #1
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    Arrow [SOLVED] Problem solving formula - results don't match

    Hi,

    My apologies if this is posted in the wrong forum. I am trying to understand the following formula:

    Code:
    p = 10 * [sqrt(n)/sqrt(k)] * [1 + log(b + 0.25)]
    Its for calculating points earned and I copied it off a games website. I knew what p, k & b were and was trying to find n. My calculations were as follows:

    Code:
    p=37.95
    k=151
    b=1
    
    p = 10 * [sqrt(n)/sqrt(k)] * [1 + log(b + 0.25)]
    37.95 = 10 * [sqrt(n)/sqrt(151)] * [1 + log(1 + 0.25)]
    37.95 = 10 * [sqrt(n)/12.29] * [1 + log(1.25)]
    37.95 = 10 * [sqrt(n)/12.29] * [1 + 0.097]
    37.95 * 12.29 = 10 * [sqrt(n)/(12.29/12.29)] * [1 + 0.097]                 // I'm not 100% confident this is right. I'm not sure whether they cancel this way
    466.406 = 10 * [sqrt(n)] * 1.097
    46.6406 = [sqrt(n)] * 1.097                                                // Divide by 10 both sides
    42.5165 = sqrt(n)                                                          // Divide by 1.097 both sides
    1087 = n                                                                   // Square both sides (rounded to nearest whole number)
    When I checked the answer on the site the answer was 1087. So I worked the formula to find p using the 3 variables:

    Code:
    n=1087
    k=151
    b=1
    
    p = 10 * [sqrt(n)/sqrt(k)] * [1 + log(b + 0.25)]
    p = 10 * [sqrt(1087)/sqrt(151)] * [1 + log(1 + 0.25)]
    p = 10 * [32.97/12.29] * [1 + log(1.25)]
    p = 10 * [2.68] * [1 + 0.097]
    p = 10 * [2.68] * [1.097]
    p = 29.3996
    The result I was expecting was p = 37.95 which is the result according to the website.

    Can someone explain if I am making a mistake somewhere? It's puzzling me since when I worked the formula to find n I got the correct answer. Thanks in advance for your help.
    Last edited by Fujo23; September 2nd 2012 at 10:50 PM. Reason: SOLVED
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  2. #2
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    Re: Problem solving formula - results don't match

    Quote Originally Posted by Fujo23 View Post
    Hi,

    My apologies if this is posted in the wrong forum. I am trying to understand the following formula:

    Code:
    p = 10 * [sqrt(n)/sqrt(k)] * [1 + log(b + 0.25)]
    Its for calculating points earned and I copied it off a games website. I knew what p, k & b were and was trying to find n. My calculations were as follows:

    Code:
    p=37.95
    k=151
    b=1
    
    p = 10 * [sqrt(n)/sqrt(k)] * [1 + log(b + 0.25)]
    37.95 = 10 * [sqrt(n)/sqrt(151)] * [1 + log(1 + 0.25)]
    37.95 = 10 * [sqrt(n)/12.29] * [1 + log(1.25)]
    37.95 = 10 * [sqrt(n)/12.29] * [1 + 0.097]
    37.95 * 12.29 = 10 * [sqrt(n)/(12.29/12.29)] * [1 + 0.097]                 // I'm not 100% confident this is right. I'm not sure whether they cancel this way
    466.406 = 10 * [sqrt(n)] * 1.097
    46.6406 = [sqrt(n)] * 1.097                                                // Divide by 10 both sides
    42.5165 = sqrt(n) // Divide by 1.097 both sides
    1087 = n                                                                   // Square both sides (rounded to nearest whole number)
    When I checked the answer on the site the answer was 1087. So I worked the formula to find p using the 3 variables:

    Code:
    n=1087
    k=151
    b=1
    
    p = 10 * [sqrt(n)/sqrt(k)] * [1 + log(b + 0.25)]
    p = 10 * [sqrt(1087)/sqrt(151)] * [1 + log(1 + 0.25)]
    p = 10 * [32.97/12.29] * [1 + log(1.25)]
    p = 10 * [2.68] * [1 + 0.097]
    p = 10 * [2.68] * [1.097]
    p = 29.3996
    The result I was expecting was p = 37.95 which is the result according to the website.

    Can someone explain if I am making a mistake somewhere? It's puzzling me since when I worked the formula to find n I got the correct answer. Thanks in advance for your help.
    I've marked in blue those values which look a little bit strange.
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  3. #3
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    Re: Problem solving formula - results don't match

    The first number you marked I divided both sides by 1.097 to remove from the right side
    Code:
    46.6406 / 1.097 = sqrt(n) * 1.097 / 1.097
    42.5165 = sqrt(n)
    The second numbers you marked is sqrt of 1087 rounded to two decimal places
    Code:
    sqrt(1087) = 32.96968304366907316174
    sqrt(1087) = 32.97
    Last edited by Fujo23; September 2nd 2012 at 10:06 PM. Reason: Left out a line in code part 1 & typo
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  4. #4
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    Re: Problem solving formula - results don't match

    42.5165 = sqrt(n) OK
    n = (42.5165) = 1807 not 1087
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  5. #5
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    Re: Problem solving formula - results don't match

    I see my mistake now - I got 1807 the first time I worked it out on paper and when I went to calculate it the other way I switched it to 1087. I even mistyped it when retyping my written work. What an obvious mistake. Thanks that was doing my head in!
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  6. #6
    Senior Member MaxJasper's Avatar
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    Re: Problem solving formula - results don't match

    It appears that Log is in base 10 and so n=1807.4
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  7. #7
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    Re: Problem solving formula - results don't match

    Yes it is log base 10 but n is always a whole number while p is rounded up to two decimal places so that's why it doesn't work out to precisely 1807.
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