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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 quantity of 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 400 given

    Total Price = 139.5
    Percentage of quantity of 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

    Please note that the percentage of quantity of item B is not constant

    Thanks in advance for any help
    Darren
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Quote Originally Posted by Unknown008 View Post
    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
    Wasn't this what you were looking for?

    In case the percentage of B is not the same as that of A, you'll have to change the second equation, that is:

    x = y

    Into the appropriate new percentage.

    If it were for example 75% of B and 25 % of A, this becomes:

    3x = y

    (where x still represents the number of items A)
    Last edited by Unknown008; September 19th 2010 at 07:33 AM. Reason: Put twice the quote...dunno what happened
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