hi my name's Amanda and I'm a pharmacist today I'm going to be talking about a type of Pharmacy calculation called allegation if you find this video helpful please press the like button subscribe to my channel and share it with others who may find it helpful too thanks I really appreciate it so we'll begin with what is allegation allegation is a method for calculating the amounts of two concentrations of the same drug needed to make a different concentration from what is available so allegation can be used for various products including liquids and creams and it's useful in compounding and I'm going to give you an example just so you can see what I'm talking about um a prescription requires 100 mlit of a 20% solution you have 50% and 10% of that solution in stock how much of each solution should be mixed to make 100 m of 20% solution so we'll solve this in a few minutes but I just want to give you an example just so you can see exactly what I'm talking about you have two concentrations of the same drug and you're going to make a different concentration using those two that you have so one concentration is stronger and one is weaker than is the desired concentration in all allegation problems so part of the difficulty in solving allegation calculations is being able to recognize them um to recognize an allegation calculation um number one there will be two concentrations available so two different strengths will be specified that are available and number two a different concentration is required to be made from those two concentrations that you have so there are two methods for solving allegation calculations I'll be covering both of these and use the one that's easiest for you um there's the ratio method and the tic-tac-toe method so first we'll look at the allegation ratio method um Step one what we're going to do is identify the high concentration which I'll refer to as HC the low concentration or LC and the desired concentration which I call DC step two we'll subtract to obtain the ratio of HC to LC so the desired concentration minus the low concentration will give us the high concentration ratio value then the high concentration minus the desired concentration will give us the low concentration ratio value so we'll just put those in the HC to LC those numbers and step three We'll add the HC ratio value and the LC ratio value to determine the total number of parts so that will give us the total number when we add those together and step four we're going to set up fractions and multiply by quantity needed like guess this will be given in the problem to obtain how much of each concentration is needed so that's just an overview of the steps to do the ratio method and now we'll look at the example that I gave you at the beginning and we'll solve that using the ratio method so the example was a prescription requires 100 milliliters of a 20% solution you have 50% and 10% of that solution in stock how much of each solution should be mixed to make 100 milliliters of 20% solution so step one we're going to identify the high concentration the low concentration and the desired concentration so HC is 50 LC is 10 and DC is 20 now we're going to subtract to obtain the ratio of HC to LC so the DC minus LC will be 20 minus 10 that will give us 10 and then the HC minus the DC will give us the LC ratio value that will be 50us 20 so that equals 30 so our HC to LC our high concentration to low concentration ratio will be 10 to 30 or you can reduce that to 1 to 3 but you don't have to reduce it you could go with the 10 to 30 but I just reduced it to keep the numbers more simple okay now in step three we're going to add the HC ratio value and the LC ratio value to determine the total number of parts so our ratio is 1 to three so one part of high con concentration to three parts of low concentration is what that ratio means and so we'll add 1 + 3 and that gives us a total gives us a total of four parts now in step four we're going to set up a fraction um and multiply by quantity needed which will be given in the problem in our problem you can see it's 100 milliliters that's how much of the final solution we need and this will help us to obtain how much of each concentration is needed okay so for our HC our high concentration um the ratio value for it is one so our fraction will be 1/4 because there are four Total Parts so 1 over 4 and then times 100 milliliters because that is our quantity um to be made and if we do the math there um we do 1 * 100 then divid by 4 give us 25 M of the high concentration which is the 50% % solution then for the low concentration our ratio value is three so three out of four 34s CU four is the total Parts time 100 millit so 3 * 100 is 300 then divid by 4 that gives us 75 milliliters of the low concentration which is the 10% and you can see that the 25 milliliters and the 75 milliliters add up to 100 milliliters so that would give us 100 milliliters of 20% solution if we mix 25 Mill of 50% solution and 75 milliliters of the 10% solution okay so now we're going to look at the allegation tic tactoe method so step one with it we're going to identify the high concentration low concentration and desired concentration and we're going to place them at the correct location in a Tic-Tac toe grid so you can see where it gets its name and the High concentration is going to go in the top left the desired concentration will go in the very center and the low concentration goes in the bottom left now for step two we're going to find the differences diagonally so we're going to find the difference between the high concentration and the desired concentration and we're going to write that um in the bottom right grid then we're going to find the difference in the low concentration and the desired concentration and we'll write that in the top right grid next we're going to add the differences vertically so we'll add the difference between the low and the desired concentration with the difference between the high concentration and the desired concentration and this will give us the total parts next we're going to determine the fraction of each needed so for the high concentration and this will be at the top we have the difference between the LC C and DC number that we have there that will be our HC part and then we will put that over the total part so that will be our high concentration fraction and then we'll do the same thing for the low concentration we'll take the number we have there in the bottom um right box that's the difference between the high concentration and desired concentration that's our low concentration part and we'll put that over the total part so that will give us our low concentration fraction now we're going to multiply each fraction by the quantity needed remember this is given in the problem and this will H allow us to obtain how much of each concentration is needed so we'll take our um High concentration fraction which is our high concentration part over our total concentration part multiply that by the quantity needed that will give us our amount of high concentration solution needed then we'll take for our low concentration fraction it's the low concentration part over the total part we'll multiply that by the quantity needed that will give us the amount of low concentration needed so now we'll go through this with an example the Tic Tac Toe method so we'll use the same example um a prescription requires 100 milliliters of a 20% solution you have 50% and 10% in stock how much of each solution should be mixed to make 100 m of 20% solution so first we're going to ident identify our high concentration desired concentration and low concentration and we'll place them in the correct location in your tic tactoe grid so remember the high concentration goes in the top left corner the desired concentration goes in the center and then the low concentration goes in the bottom left now we're going to find the differences diagonally so with the high concentration the difference between 50 and 20 give us 30 and we'll put that in the bottom right and then diagonally for the low concentration the difference between 10 and 20 that gives us 10 and we'll put that in the top right next we're going to find the total parts and we'll do this by adding the differences vertically so we have 10 + 30 and that gives us 40 so 40 is our total parts now we're going to determine the fraction of each needed so for the high concentration um it's a to it's 10 parts out of the out of 40 is our total parts so our high concentration fraction is 10 out of 40 and for the low concentration we have 30 parts out of the total 40 parts so it's 30 out of 40 now we're going to multiply each fraction by the quantity needed that's given in our problem which is 100 milliliters in this problem and this will allow us to to obtain how much of each concentration is needed so our high concentration fraction was 10 out of 40 so times 100 milliliters so you can do that 10 * 100 which is 1,00 / 40 = 25 milliliters of the 50% Solution that's our high concentration and then the low concentration fraction was 30 out of 40 so 30 * 100 um that gives us 3,000 / 40 that equals 75 M so that we'll need 75 M of a low concentration solution which is the 10% solution and you can see we got the same exact answer uh just a little bit different methods of doing it but you can see you add the 25 milliters and the 75 milliliters that gives us 100 milliliters total and that will of 25 M of the 50% solution plus 75 M of the 10% solution tion that will give us 100 m of 20% solution so now we'll just go over a summary and some key points to remember um remember allegation is a method for calculating the amounts of two concentrations from the same drugs needed to make a different concentration from what's available um one concentration is stronger or higher I refer to this as HC and one is weaker or lower this will be LC low concentration than the desired concentration which is DC and allegation problems can be solved using the ratio method or the tic-tac-toe method use the one that makes the most sense for you and both allegation methods are ways to determine the amounts of the high concentration and low concentration needed to make the desired concentration um just a summary of the ratio method steps you're going to identify the high concentration low concentration and desired concentration from the problem subtract to obtain the high concentration to low concentration ratio and to get this you'll take the DC minus the LC that will give you the HC ratio value then you'll take the HC minus the DC and that will give you the LC ratio value um next you'll add the HC and LC ratio values to obtain the total parts and then set up fractions and multiply by the quantity needed so you'll set up a fraction with the low concentration ratio value over the total parts and multiply that by the quantity needed that will give you your low concentration quantity amount and then for the high concentration ratio value over the total Parts times the quantity needed that will give you your high concentration quantity amount and then a summary for the Tic Tac Toe method um first you'll identify the high concentration low concentration and desired concentration and place them in the Cur correct location in the T tict tactoe grid remember the high concentration goes in the top left the desired concentration goes in the center and the low concentration goes in the bottom left then you're going to find the differences diagonally write those numbers in the grid then add the different parts add add the differences vertically to get the total parts and then you'll determine the fraction of the high concentration which will be across the top and the low Concentra ation which will be on the bottom and you'll just put the high concentration amount over the total parts and the low concentration amount over the total parts that will give you those fractions and then multiply each fraction by the quantity needed which like I said before it's it's specified in the problem thanks for watching please like and share this video with others who may find it helpful and please subscribe to see more of my drug information videos thank you