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Math Help - Calculating added percentages

  1. #1
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    Calculating added percentages

    Hello everyone, I imagine this has been queried before but I've not been able to find a clear understandable (to maths dummy me) answer, if someone could help I'd be grateful.

    I have to invoice a fee to a Japanese client which includes 20% tax which the Japanese government deducts at source. i.e. 20% will be deducted from the total invoice amount, not the fee I'm to receive.

    eg. say my fee is 10,000 yen. If I calculate 20% of that and invoice 12,000 yen the total value of the invoice has increased. The tax office would deduct 20% from 12,000 yen, so I'd only receive 9,600 yen.

    So how do I calculate the correct percentage?

    Many thanks!
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  2. #2
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    12,000 \times x = 10,000

     x = \frac{5}{6}

    You can use this  \frac{5}{6} as your multiplier
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  3. #3
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    Thank you pickslides, I'm sorry but I still don't understand, could someone clarify?

    Many thanks!
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  4. #4
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    I think pickslides misunderstood your question.

    If I understand the question correctly, you want to set your fee so that after 20% is subtracted, you will have $10000.

    Let "x" be the amount charged. The 20% of that is 0.20x. After subtracting that you will have left x- 0.20x= (1- .20)x= 0.80x= 10000.

    Solve for x by dividing both sides by 0.80: x= 10000/0.80= 12500
    You should charge $12500.

    Then 20% of 12500= 0.20*12500= 2500 and 12500- 2500= 10000.
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  5. #5
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    HallsofIvy, thank you! That's exactly what I was looking for.
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