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Pharmacy Calculations – Deciphering Word ProblemsFocus on what you’re solving for; ignore the extra details.What is the dose? (Chapter 13)250mg=Dose drug amountDrug Strength1 tspAmount to make (volume)Example: If a prescription reads: Cefaclor 250 mg/5ml, dispense 150 ml, 375 mg b.i.d. x 10d, what is the dose in teaspoonsful? (Problem #41, page 100)250mg=375mg1 tspX tsp250x=375X=1.5 tspnown values:Drug strength (250 mg/5ml)Dose drug amount (375 mg)Solve for Amount to make (volume)Answer: 1.5 tsp per doseLooking for a shortcut to cross-multiplying? Rather than write out the full equation and each step, try using this method with you calculator:Step 1: Multiply the two numbers that are diagonal from each other (just think-when two get together, they multiply)250mg=375mg1 tspxStep 2: Divide the answer from step 1 by the number that is diagonal to the variable you’re solving for (just think-the lonely one will try to split up or divide the couple). X = Step 2’s answerHow much of a drug do you need? (Chapter 16) These questions may require you to do an additional step if they want the answer in the form of how many tablets/capsules of a particular strength (how many tablets of the drug do you need to make...?). 3 gm=X 500mltotal amount to make Example: A prescription is written for allopurinol liquid 20 mg/ml in Ora-Plus:Ora-Sweet 1:1 (label with a shelf life of 60 days). How many tablets of allopurinol 100 mg are needed to prepare 150 ml? (Problem #4, page 121)20mg=Xmg1 ml150mlX=3000mg *STEP 1If each tablet is 100mg, how many tablets are needed? =3000/100 or 30 tablets *STEP 2Known values:Drug strength (20mg/ml)Total amount to make 150ml Strength of available drug 100mgStep 1: Solve for Dose StrengthStep 2: Solve for # of tablets needed of available drug. If the drug strength is given as a %:*Percent roughly means “out of each one hundred” so any percentage can be depicted as a fraction where the percentage is the numerator (number on top) in the unit of grams and “100” is the denominator (number on bottom) in the unit of ml or grams. That percentage is the drug’s strength. %=strength100amountExample: A prescription is written for Dilantin 5% in zinc oxide qs 120 g. How many Dilantin 50 mg tablets are needed to prepare this compound? (Problem #5, page 121)5g=Xmg100 g120gX=6g *STEP 1If each tablet is 50mg, how many tablets are needed? =6g/50mg or 6000mg/50mg or 120 tablets *STEP 2Known values:Drug strength (5% or 5g/100ml)Total amount to make 120 gStrength of available drug 50mgStep 1: Solve for total strengthStep 2: Solve for # of tablets needed of available drugHow many days supply is this? (Chapter 17)Days supply =Rx MaxDaily doseExample: How many days supply is the following prescription?: Augmentin 500 mg #42 one t.i.d. (Problem #2, page 129)Known values:Rx Max (42 tab)=42 tab3 tab/day=14 daysDaily dose (3 tab/day)Each tablet is 500 mg (irrelevant to this problem)Solve for days supplyAnswer: 14 daysWhat is the amount insurance plans will allow per fill? (Chapter 18) These questions require multiple step calculations.Step 1: Calculate the Rx MaxStep 2: Calculate the amount in an insurance period (usually 34 days), This is the initial fill quantity (if it’s less than the Rx Max)Step 3: Calculate how many refills/partials would be allowed to meet Rx MaxRules of Thumb to Remember:Do not split up boxes, bottles or vialsIn the case of bottles, insurance will usually only allow 1 bottle to be dispensed at a time even if it provides less than the amount in an insurance periodExample: Dicyclomine 20 mg #200, 20 mg p.o. qid, 1 refill (Problem #14, page 141)Known values:Amount to dispense=200 tabletsNumber of fills=2 (remember to count initial fill as first fill, so a Rx that states 1 refill=2 fills)Daily dose=4 tablets, 20mgx4= 80mgDose=20mgStep 1: Calculate the Rx MaxRx Max = #(amount to dispense) x # of fills =200 x2 =400 maxStep 2: Calculate the amount in an insurance period (34 days in most cases)Amount in an insurance period=34xdaily dose=20mg=1 tab, qid=4 times/day, 1x4=4 tab/day= 34x4=136 tabs, Initial fill quantityStep 3: Calculate how many refills/partials would be allowed to add up to Rx Max=Rx Max (Calc found in Step 1)Amount in insurance period (Calc found in Step 2)=400 tabs=2.94136 tabsSo, 2 full qty fills plus a partial are required to meet Rx MaxIn other words 1 initial fill of 136, 1 refill of 136 and a partial fillTo determine partial fill quantity:Rx Max – (Initial fill qty x 2) (2 is the whole number from above calc)400-(136x2)=400-272=128=Partial Fill AmountDouble check your work by adding up quantities in initial fill, all refills and partial fills. These should equal the Rx Max.136 (initial fill) + 136 (1 refill) + 128 (partial refill)=400Compounding Fees (Chapter 20)Formula to calculate cost to compound:60 min=Min it took to compound $ hourly salaryCost to compound $Add cost to compound to cost of materials(Ratio & Proportions) How many ml should be dispensed?, What is the dose that the patient received? (Chapter 27) In a simple ratio & proportion problem, there are 4 elements. Usually 3 are known & you solve for the 4th.mg=Amount of drug mlTotal amount to makeDrug strength = Specific Dose500mg=350 mg20mlX ml500X=7,000X=14 mlExample: How many ml of aminophyllin solution (500mg/20ml) is needed to prepare 350 mg aminophyllin in 100 ml of D5W? (Problem #17, page 214)Known values:Drug strength (500mg/20ml) Amount of drug (350mg)Diluent (100ml of D5W)-irrelevant to this problemSolve for total amount to makeAnswer: 14 mlExample: A patient is given 10.8 ml of phenytoin as a loading dose. Phenytoin is available as 50 mg per ml in 2 ml and 5 ml vials. What is the dose in mg that the patient received? (Problem #25, page 215)50mg=X mg1ml10.8 mlX=540 mgKnown values:Drug strength (50mg/1ml)Total amount to make (10.8ml)Available vial sizes 2ml & 5 ml-irrelevant for this problemSolve for Amount of drugAnswer: 540 mgPowdered Drug Preparations (Chapter 28)diluent volume + powdered volume = total volumeSometimes a 2 step process:provided 2 out of 3 of the volumes above, solve for third volumeWhat’s the final concentration of the drug?Problem may provide how much you’re putting that dose into-irrelevant to the problem at hand-first you have to determine the dose.Example: You add 10 ml of sterile water for injection to 1 g of a drug that has a powder volume of 0.8ml. What is the concentration of the drug in mg/ml in the final solution? (Problem #7, page 224)Known values:Diluent volume (10 ml)Powder volume (0.8ml)Amount of drug (1 g)Solve for concentration of final solutionStep 1: Calculate total volumeDiluent volume + powder volume = total volume10 ml + 0.8 ml = 10.8 mlStep 2: Calculate concentration of final solutionConcentration is g/1ml or ml/1ml or g/1gAmount of drug=1 g=1,000mg=92.6 mgTotal volume10.8 ml10.8ml1 mlAnswer: 92.6 mg/mlExample: A 1.5 g vial of antibiotic has a powder volume of 1.4ml. You need a concentration of 125 mg/ml. How many ml of sterile water for injection will you need to add to obtain this concentration? (Problem #17, page 225)Step 1: Calculate total volume based on concentration125 mg=1.5g or 1500mg1 mlX (total volume)12 ml=xStep 2: Calculate diluent volume based on powder volume & total volumeDiluent volume + powder volume = total volumeX + 1.4ml=12mlX=12ml-1.4mlX=10.6mlExample: 5 g of the medication (powder volume=0.7ml) is reconstituted with 9.3 ml of sterile water for injection. Then 3 ml of an antibiotic is added to a 50 ml IVPB. How many g of the medication was added to the IVPB? (Problem #43, page 230-problem mis-worded in book)Step 1: Calculate total volumeDiluent volume + powder volume = total volume9.3 ml + 0.7ml = 10ml Step 2: Calculate the amount of drug that was in the 3ml that was added to the IVPB5g=x10 ml3 ml1.5g=XDrug Strength in Percentages (Chapter 29)% strength is always grams100 mlExample: What percent strength solution would result if you mixed 3 g of NaCl in enough water to make 25 ml? (Problem #2, page 235)3g=X %25 ml100 ml12%=XExample: How many grams of glucose are contained in 1,500ml of a 10% glucose solution? (Problem #10, page 236)10g=X grams100 ml1,500 ml150 g=XRatio Solutions (Chapter 30)First number of a ratio is typically 1 (sometimes a 2). Ratios are always in units:g:mlml:mlg:gTo convert a ratio to a fraction:Place first number in numeratorPlace second number in denominatorEx: 1:20 becomes 1/20To convert a ratio to a percent:First number=X%Second number100mlSolve for XEx: 1:20 1=X%20100ml5%=xTo convert a percent to a ratio:Place the percentage in the first number field and 100 in the second number fieldDivide both sides of the ratio by the first number (this will make the first number a 1)Ex: 0.08% becomes 0.08g:100ml which becomes 1:1,2500.08g:100ml0.080.081g:1,250Example: You need to prepare 750 ml of a 1:500 w/v potassium permanganate solution. How many g are needed? (Problem #4, page 245)1g=X g500ml750ml1.5g=xExample: Adrenalin injection is also available as a 1:100,000 w/v strength. Express this concentration in mcg/ml. (Problem #22, page 247)1g=1000mg=1mg=1,000mcg=10mcg100,000ml100,000ml100ml100mlmlDosage Calculations Based on Body Weight (Chapter 31)1 kg = 2.2 lbExample: A patient weighs 44 pounds and is receiving ampicillin at a rate of 100 mg/kg/day. What is the total daily dose in grams?Step 1: What is the patient’s weight in kg?44 lbs=20 kg2.2 kg/lbStep 2: Calculate the dose based on the rate & patient’s weight.100 mgx20 kg=2,000 mg=2 gKg/daydayDosage Based on Body Surface Area (Chapter 32)A Nomogram chart is used to calculate body surface area (BSA) as a function of height and weight. Either the BSA will be provided in the problem, or the weight & height are provided along with a Nomogram and you determine the BSA on the Nomogram.BSA unit of measure is m2. This unit of measure is cancelled out thru the math. Example: A patient with a BSA of 2.1 m2 is to receive 7.5 mg/ m2/week of methotrexate. The MTX is available as 25mg/ml. How many ml are needed for the weekly dose? (Problem #45, page 274)Known values:Patient’s BSA (2.1 m2)Weekly dose amount (7.5 mg/ m2)Available Drug strength (25 mg/ml)Step 1: Calculate total drug needed based on BSA.7.5 mg=X mg1 m22.1m215.75 mg=XStep 2: Calculate how many ml will deliver that total drug amount based on available drug strength25 mg=15.75 mg1 mlX0.63 ml=XInfusion Rates/Drip Rates (Chapter 33) There are a couple ways to complete these calculations.Method A: Multiply a series of fractions, placing like-units diagonal from each other so they cancel out & you’re left with the desired unitsMethod B: Use a series of equations, using ratio & proportion to cross multiply solving for the unknown as we have been solving most problems.Example: Calculate the infusion rate in ml/hr for a drip, concentration 5g/500ml. The rate is 25 mcg/kg/min. The patient weighs 112 kg. (Problem #13, page 281)Known values:Drug strength (5g/500ml)Infusion rate (25 mcg/kg/min)Patient’s weight (112kg) Solve for Infusion rate in ml/hrAdditional known values (60 min/1 hr, 1,000 mg/mcg, )Method A:25mcgx112kg=2,800mcg, 2,800 mcgx1 mg=2.8 mg,Kg/min11 min1 min1,000 mcg1 min Then,2.8 mgx60 min=168 mg, 168 mgx500 ml =16.8 ml1 min1 hr1 hr 1 hr5,000 mg (which is 5 g) 1 hrMethod B:Step 1: Solve for the rate based on patient’s weight25 mcgx112 kg=2,800 mcgKg/min11 minStep 2: Convert 2,800 mcg to g (since the drug strength is in grams)2,800 mcg = 2.8 mg = 0.0028 g Step 3: Calculate the rate in grams per hour (1 hr = 60 min)0.0028 g=X1 min60 min0.168 g=XSo, the rate is 0.168 g/60 min or 0.168g/1 hrStep 4: Calculate how many ml will deliver 0.168 g of the drug based on the strength.5 g=0.168g500 mlX16.8 ml=XDilutions (Chapter 34)When you dilute a drug, that means the amount of the drug in the solution remains constant, but the volume of that solution increases. Therefore, there’s an inverse proportion between the volume and the % strength of a drug within a solution.What’s the final percentage strength of a drug when it’s diluted with an amount of diluent? ................
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