Percentage in that respect means partsofactiveingredientper100partsoftotalpreparation.The three basic rules to remember in solvingpercentage problems are:1. To find the amount of the active ingredientwhen the percentage strength and the totalquantity ARE known, multiply the totalweight or volume by the percent (expressedas a decimal fraction).Example: Substance X contains 38% fat. Howmany grams of fat are required to prepare120 g of substance X?Solution: 38% is expressed as a decimal frac-tion 0.38 and multiplied by the amount of thefinished product required.45.60g—the weight of fat needed.2. To find the total quantity of a mixturewhen the percentage strength and theamount of the active ingredient are known,divide the weight or volume of the activeingredient by the percent (expressed as adecimal fraction).Example: If a mixture contains 20% ofsubstance Y, how many grams of the 20% mix-ture would contain 8 g of Y?Solution: 20% is expressed as a decimal frac-tion 0.20. Divide the weight (8 g) by thethus;3.40.0 g, the weight of 20%mixture that wouldcontain 8 g ofsubstance Y.percent,To find the percentage strength when theamount of the active ingredient and thetotal quantity of the mixture are known,divide the weight or volume of the activeingredient by the total weight or volume ofthe mixture. Multiply the resulting answerby 100 to convert the decimal fraction topercent.Example: Find the percentage strength of Zif 300 g of a mixture contains 90 g of substance Z.Solution:0.3 g, is the percent of Zexpressed as adecimal fraction.
of Z in the mixture.Alternate Method for Solving PercentageProblemsThe alternate method for solving percentageproblems incorporates the three rules discussedabove into one equation. This method is oftenpreferred since it eliminates errors that may resultfrom misinterpreting the facts given in theproblem.1. Percent strength = Amount of activeingredient x 100(%)Total amount ofpreparationExamples:a. Calculate the percent of A in a solution if120 g of solution contains 6 g of A.Solution: Substitute the known facts in theequation and use X for percent (the unknownfactor).Therefore X = 5, which is the percent strengthof the solution.b. Calculate the amount of active ingredientm 300 g of a 5070 mixture of active ingre-dient B.Solution: Convert 5% to a decimal fraction0.05. Substitute the known facts in the equationsand use X for the amount of active ingredient(unknown).2. A variation of equation 1 uses “parts perhundred” instead of percent with X usedas the unknown.Amount of activeingredientAmount of totalpreparationParts of activeingredient= 100 parts (totalmixture)8-8

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