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Math Help - Need an equation for an energy Calculation

  1. #1
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    Jan 2009
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    Need an equation for an energy Calculation

    Money spent on gas = A (Dollars)

    Night Time Unit rate = B (cents/KwH)

    Day Time Unit Rate = C (cents/KwH)

    The night time unit rate B is expressed as a % Y of the total Kwh for the money spent A

    I need to know the number of KwH for B and C

    For Clarity below I have shown an example of the reverse calculation

    Total KwH (Z) 4702
    Y% 55
    Night Time KwH 2586.1 (Z*Y/100)
    Night Time Unit Rate (B) 4.5
    Night Time Money 116.3745 ((B/100)*(Z*Y/100))
    Day Time KwH 2115.9 (Z*(100-Y)/100)
    Day Time Unit Rate (C) 11.87
    Day Time Money 251.15733 ((C/100)*(Z*(100-Y)/100))

    This is a KwH to Money Conversion

    I have been trying for a week now to come up with a formula for Money to KwH conversion

    Thanks in advance for any help provided
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  2. #2
    Senior Member
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    Dec 2007
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    Melbourne
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    Let b= B/100 and c = C/100. then

    Z = \frac{A}{bY+c(100-Y)}
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  3. #3
    Newbie
    Joined
    Jan 2009
    Posts
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    Problem Resolved

    Thanks for that Badgerigar - your answer was actually incorrect but your thinking was spot on as it sent me down the right track.

    The actual answer was

    Z=((b*Y)+c*(100-Y))*A/100

    Thanks it was in front of my nose all the time - long time out of high school

    Thanks again
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  4. #4
    Senior Member
    Joined
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    Melbourne
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    You can test formulas like these by taking a simple example. If we spend 4.5c on energy at night, the formula should give 1 kWh.

    So A = 0.045, B = 4.5, C = 11.87, Y = 100.

    b = 0.045 and c = 0.1187

    Then plugging into your formula
    Z=((0.045*100)+0.1187*(100-100))*0.045/100
    entering this into a calculator gives
    Z=0.002025
    which is wrong, because 4.5c should have bought exactly one kWh.

    checking my answer, I noticed that A was in dollars while B and C were in cents. This means my answer was also wrong. The correct formula should be

    Z = \frac{10 000A}{BY+C(100-Y)}

    Sorry to confuse you.
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