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    Tonyclev

    Formula For A Percentage From An Unknown Number That Has Tax (7.75%) And Tip (15%) Added To It. Can You Help?

    I am trying to get a formula to determine the cost of a menu item that original price includes tax and tip. If the menu price is $6.50 and includes tax(7.75%) and tip(15%) how would I calculate (Other then trial and error, which is what I have been doing) what the price is without the tax and tip. It is NOT $6.50 minus 22.75%, since the tax and tip is put on the unknown number not on the $6.50.

    asked 4 months ago

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    Dinnydowd

    If you take the $6.50 and divide it by 1.2275 (which is 1.0 + .15 tip+ .0775 tax), you'll get the original amount. In this case, I get $5.2953, which you could round to $5.30......That should always work. You can multiply the $5.2953 by 1.2275 to confirm that it equals the $6.50 (rounded off).

    answered 4 months ago   

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      Oddman

      Sometimes, the tip is computed from the value of the bill that includes the tax. In that case, the math might look like this:
      (item_cost)*(1+7.75%)*(1+15%) = 6.50
      (item_cost)*(1.0775)(1.15) = 6.50
      item_cost = 6.50/(1.0775*1.15)
      item_cost = 6.50/1.23915
      item_cost = 5.2456... Or $5.25.

      Check: 5.25 + tax = 5.25(1.0775) = $5.66
      5.66 + tip = 5.66(1.15) = 6.51.  In both cases we rounded up.

      Try: 5.24 + tax = 5.65
      5.65 + tip = 6.50.  Again, we rounded up in both cases.

      $5.24 + tax + tip will result in a charge of $6.50.

      answered 4 months ago   

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