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Math Help - Formula for Calculating original quantities from a price

  1. #1
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    Formula for Calculating original quantities from a price

    Hi I need a formula to solve the following problem, unfortunately my maths is pretty basic.

    Item A = 0.23 per unit up to and including first 150 units
    Item A = 0.18 per unit above 150 units
    Item B = 0.15 per unit
    Item A Quantity = 400 = (150 * 0.23) + (250 * 0.18) = 79.5
    Item B Quantity = 400 * 0.15 = 60.0
    ----
    Total Price = 139.5
    ----

    Now if we have the Total Price, the percentage of the total price which was spent on Item B and the above per unit rates
    how do you calculate what quantity of each item was brought originally.
    It should be possible to get back to Item A Quantity 400 and Item B Quantity 300 given

    Total Price = 139.5
    Percentage of Total Price spent on Item B = 50%
    Item A = 0.23 per unit up to and including first 150 units
    Item A = 0.18 per unit above 150 units
    Item B = 0.15 per unit


    Thanks in advance for any help

    Darren
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  2. #2
    Junior Member RHandford's Avatar
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    Hi

    First the % spent on B was not 50%.

    However if you know the % you can do the following:
    For B quantity=% of total value/unit price

    For A:
    First rough guess by doing remaining total value/0.23
    If the result is > 150 (and in this case it is) then you have at least 150*0.23
    so for the remainder (total value remaining-(150*0.23))/0.18

    Hope that makes sense
    Last edited by RHandford; September 16th 2010 at 01:43 AM. Reason: Typo
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  3. #3
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    Thanks for the answer, however in my haste I got the % wrong. I actually meant given the % of the quantity which was Item B, so it should have been

    Total Price = 139.5
    Percentage of quantity for Item B = 50%
    Item A = 0.23 per unit up to and including first 150 units
    Item A = 0.18 per unit above 150 units
    Item B = 0.15 per unit

    So from the Total order 50% of the quantity consisted of Item B

    Darren
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  4. #4
    MHF Contributor Unknown008's Avatar
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    Hm, let's define variables.

    Let x be the number of items A.
    Let y be the number of items B.

    We know that Price for A = 0.23n (for n\leq 150) + 0.18(x - n)
    Price for B = 0.15y

    Now, total gives:

    0.23 n + 0.18(x-n) + 0.15y = 139.5

    Second equation:
    x = y

    Substituting in first equation:

    0.23n + 0.18(x - n) + 0.15x = 139.5

    Assuming that there is less than 150 items of a, makes x - n = 0 and x = n
    0.23x + 0 + 0.15x = 139.5
    x = 367

    But x should have been less than 150!

    So, we know that x is greater than 150, so, n = 150

    0.23(150) + 0.18(x - 150) + 0.15x = 139.5
    34.5 + 0.18x - 27 + 0.15x = 139.5
    0.33x = 132
    x = 400

    So, y = 400
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