RESOLVED - Math Question (Discounts and such)

Hello all,
This pertains to processing sales orders for a retailer.
A dollar or percentage discount can be given to an individual item in an order.
On top of that, a percentage discount can be given to the order as a whole (in which case, this percentage off is applied to each individual item in the order).

Let's say an item costing $100 is discounted $20. So the price of the item at this point is now $80.
At the end of the sale, a 30% overall discount is applied to the order. So now 30% off of the $80 (not $100) is taken for the item described above, thus discounting the item $24 more.
So the total amount off of the item is $44, and the customer pays $56 for that item.

Now - if at some later time, we wanted to look at data to reconstruct what happened on that sale, would it be possible to do so given only these three pieces of information:
Regular Price of Item = $100
Total Amount Off = $44
Order Level Discount = 30%

In other words, is there an equation that can be used to determine what portion of the $44 was a result of the 30% discount, and portion was the dollar discount?

Would it not make more sense and be easier to not store the $44 but store the amount of the discount or discounted price instead. i.e. $20 or $80

not something like x + (100 - x)*0.3 = 44 ? -

Quote:

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Originally Posted by i-and-i

not something like x + (100 - x)*0.3 = 44 ? -

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Checked at www.mathportal.org/calculators/solving-equations/polynomial-equation-solver.php?val1=x+plus+(100+-+x)%2A(30/100)+&val2=44&val3=xplus%5Cleft(100-x%5Cright)%7B%5Ccdot%7D%5Cdfrac%7B30%7D%7B100%7D%3D44

I-and-I and dbasnett: thanks very much, I thought it might be something along those lines, but couldn't quite formulate it (what can I tell ya, it's been more years than I care to mention since I had algebra class). Now all I have to do is come up with some VB code to handle this ...

Well, I'm not too proud to ask - what would the VB code look like to solve that equation?

Quote:

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Originally Posted by BruceG

Well, I'm not too proud to ask - what would the VB code look like to solve that equation?

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If you want to work with sales stuff you will probable work with decimals, so declare 4 doubles (give them the values you want) and just translate the formula to an x = ... ?

Basically, I need a function that solves for "x" (x being the DollarAmountOff), where
x + ((RegularItemPrice - x) * OrderLevelDiscount) = TotalAmountOff

quick and dirty (my data types aren't exactly right):

Code:

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Private Sub btnCalc_Click(sender As System.Object, e As System.EventArgs) Handles btnCalc.Click
        Dim regPrice As Integer
        Dim totalOff As Single
        Dim olDiscount As Single
        Dim itemDiscoutAmt As Single
        Dim orderDiscountAmt As Single

        regPrice = 100
        totalOff = 44
        olDiscount = 0.3

        itemDiscoutAmt = regPrice - (regPrice - totalOff) / (1 - olDiscount)
        orderDiscountAmt = totalOff - itemDiscoutAmt
    End Sub

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vbfbryce - thanks very much, that helps me out.
Thanks again to all for your help.

Quote:

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Originally Posted by BruceG

Well, I'm not too proud to ask - what would the VB code look like to solve that equation?

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Code:

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    'based on the example
    'cash discount - x
    Dim cashDisc As Decimal

    'item price
    Dim itemPrice As Decimal = 100D

    'total off
    Dim totOff As Decimal = 44D

    'order discount
    Dim ordDisc As Decimal = 0.3D

    Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click
        'x + (itemPrice - x) * ordDisc = totOff
        'distribute
        'x + (itemPrice * ordDisc) - (x * ordDisc) = totOff
        'x - (x * ordDisc) + (itemPrice * ordDisc) = totOff

        'combine like terms
        'x - (x * ordDisc) in our exaqmple is .7x
        Dim tempCD As Decimal = 1 - ordDisc
        Dim tempIO As Decimal = itemPrice * ordDisc 'itemPrice * ordDisc
        'isoalte variable
        'tempCD*x + tempIO = totOff
        'tempCD*x  = totOff - tempIO
        '(tempCD*x)/tempCD  = (totOff - tempIO)/tempCD
        Dim tempTO As Decimal = totOff - tempIO
        'x  = (tempTO)/tempCD
        Dim x As Decimal = tempTO / tempCD
        Debug.WriteLine(x)
    End Sub

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Use the debugger to step through this. One piece of advice, use Decimal for money.