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Thread: A+B=C Solve for A when B is % based on A

  1. #1
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    A+B=C Solve for A when B is % based on A

    I feel like this is so simple but I just can't seem to pull it out of the aging brain......

    I have a Product Cost represented as A
    I have a Fee for the product that is a percentage of the Product Cost as B B=(A*.10)
    This gives me the Total Cost of the product as C

    Now if I know the Product Cost is 500.00 A=500
    If the Fee is 10% of the Product Cost then 500*.10=50 B=50 (the Percentage is not always constant and can change but it is always based on the product cost of A)
    A+B=C
    500+50=550 C=550

    However, if I don't know the Product Cost but am only given the Total Cost and the Fee, How can I find out what the Product Cost is?
    C=A+B
    or
    C=A+(A*.10)
    How do I solve for A?


    Thanks in advance
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  2. #2
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    Re: A+B=C Solve for A when B is % based on A

    $A + B = C$

    $A + pA= C,~\text{where $p$ is the percentage used to obtain $B$}$

    $(1+p)A = C$

    $A = \dfrac{C}{1+p}$
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  3. #3
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    Re: A+B=C Solve for A when B is % based on A

    I know this probably seems very simplistic but it is a very deep part of a more complicated excel formula and I'm afraid I could see the Trees for the Forest.
    Excel got in the way!!
    I couldn't see the math for the excel!!

    thanks so much!!
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  4. #4
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    Re: A+B=C Solve for A when B is % based on A

    Quote Originally Posted by lisach View Post
    I know this probably seems very simplistic but it is a very deep part of a more complicated excel formula and I'm afraid I could see the Trees for the Forest.
    Excel got in the way!!
    I couldn't see the math for the excel!!

    thanks so much!!
    I've been in those excel forests before... good luck!
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