2. To find the total quantity of a mixture whenthe percentage strength and the amount ofthe active ingredient are known, divide theweight or volume of the active ingredient by thepercent (expressed as a decimal fraction).3. To find the percentage strength when theamount of the active ingredient and the totalquantity of the mixture are known, divide theweight or volume of the active ingredient by thetotal weight or volume of the mixture. Thenmultiply the resulting answer by 100 to convertthe decimal fraction to percent.ALTERNATE METHODS FOR SOLVINGPERCENTAGE PROBLEMSThe alternate method for solving percentageproblems, illustrated below, incorporates the threerules discussed above into one equation. This methodis often preferred since it eliminates errors that mayresult from misinterpreting the values given in theproblem.% strength = Amtofactiveingredientx100(%)Total amt of preparationA variation of the alternate percentage equation,illustrated below, uses “parts per hundred” instead ofpercent, with X used as the unknown.Amt of active ingredient = Parts of active ingredientAmt of total preparation 100 parts (total mixture)RATIO AND PROPORTIONCALCULATIONSRatio is the relationship of one quantity to anotherquantity of like value. Example ratios are 5:2, 4:1.These ratios are expressed as “5 to 2” and “4 to 1,”respectively. A ratio can exist only between values ofthe same kind, as the ratio of percent to percent, gramsto grams, dollars to dollars. In other words, thedenominator must be constant.6-14Example: If a mixture contains 20% of substance Y,how many grams of the 20% mixture would contain 8 gof Y?Solution: 20% is expressed as a decimal fraction(0.20). Divide the weight (8 g) by the percent, thus:40.0 g , the weight of 20%.20 ) 8.00 mixture that would8 0contain 8 g of00 substance Y.Example: Find the percentage strength of Z if 300 gof a mixture contains 90 g of substance Z.Solution:0.3 g , is the percent of Z300 ) 90.00 expressed as a decimal90fraction000.3 x 100(%) = 30% of Z in the mixtureExample #2: Calculate the amount of active ingredientin 300 g of a 5% mixture of active ingredient B.Solution: Convert 5% to a decimal fraction (0.05).Substitute the known values in the equations, and use Xfor the amount of the unknown ingredient .0.05 = X/300X = 15 gExample #1: Calculate the percent of A in a solution if120 g of that solution contains 6 g of A.Solution: Substitute the known values in the equationand use X for the percent (the unknown factor).X = 6/120 x 100(%) = 5 (%)Therefore, X = 5, which is the percent strength of thesolution.Example: Ascertain the percent B in a mixture of600 g that contains 15 g of B.Solution:=X = 2.5, the parts of active ingredientper 100 parts of total mixture, or2.5%15600=X100600 X = 1500X =1500600