# Complex / Doris Turner Med Math Questions

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1 Complex / Doris Turner Med Math Questions 1. Problem type: IV infusion rate + infusion pump Medication: azithromycin PROBLEM Suppose Mrs. Turner s orders call for 500 mg of azithromycin to be administered intravenously for community acquired pneumonia. The solution has been diluted to a concentration of 2 mg/ml and needs to be administered over 1 hour. At what rate should the infusion pump be set? Start by figuring out how many milliliters will be needed to administer the ordered dose. 1. Determine how many milliliters of the concentration will be delivered to administer the ordered dose. 500 mg x 1 ml = 250 ml 2 mg 2. Divide the total number of ml needed to deliver the 500 mg by the expected duration of 1 hour. 250 ml = 250 ml/hr 1 hr Number: 250 Units / Rate: ml/hr

2 2. Problem type: Dosage calculation + Stock on hand Medication: venlafaxine PROBLEM Mrs. Turner s daily medications include venlafaxine extended release, 150 mg, by mouth, once a day. However, the hospital pharmacy only carries 75 mg extended release tablets. How many tablets of venlafaxine extended release should be administered to her? You can use the equation below, where X is the number of tablets that should be administered. D (ordered dose ) x Quantity = X H (dose on hand) 1. Determine what information you have. D (ordered dose) = 150 mg H (dose on hand) = 75 mg Q (quantity) = 1 tablet 2. Plug into the equation and solve. D (150 mg ) x 1 tablet = X H (75 mg) X = 2 tablets Number: 2 Units: tablets

3 3. Problem type: Total daily dosage Medication: hospital hypothetical Suppose Mrs. Turner s provider updated her order for 325 mg, 2 tabs, by mouth q6h PRN temp. > F to 325 mg, 2 tabs, by mouth q4h PRN temp. > F. The Davis s Drug Guide reports that acetaminophen has a maximum recommended dosage of 4 g/day. How many doses can Mrs. Turner take without exceeding the recommended maximum dosage? There are 1000 mg in one gram. 1. Determine how many milligrams are in 4 grams. 4 g x 1000 mg = 4000 mg 1 g 2. Determine how many 325 mg tablets go into 4000 mg mg x 1 tablet = 12.3 tablets 325 mg 3. Round down to the nearest whole tablet = 12 tablets 4. Divide the total number of tablets by the number tablets in a dose. 12 tablets total x 1 dose = 6 doses 2 tablets Number: 6 Units: doses

4 4. Problem type: Total daily dose calculation Medication: hospital PROBLEM Suppose Mrs. Turner s current temperature is F. For temperatures greater than F, the prescriber s order allows acetaminophen, 325 mg, 2 tabs, by mouth, every 6 hours. Assume that on her first day of hospitalization, Mrs. Turner s temperature is greater than F three times. How many grams of acetaminophen will she have ingested on her first day of hospitalization? Round your answer to hundredths. Multiply the number of taken doses by the number of tablets. 1. Multiply the number of doses taken by the number of tablets per dose. 3 doses x 2 tablets = 6 tablets 1 dose 2. Multiply the dosage of acetaminophen by the number of tablets. 6 tablets x 325 mg = 1950 mg 1 tablet 3. Convert the total daily milligrams to grams mg x 1 g = 1.95 g 1000 mg Number: 1.95 Units: g

5 5. Problem type: Dosage calculation + Stock on hand Medication: potassium chloride PROBLEM Mrs. Turner s daily medications include potassium chloride, 10 meq tablet by mouth once daily. The hospital pharmacy will dispense potassium chloride liquid 10% (1.5 gram or 20 meq per 15 ml). The KCl liquid will be further diluted in a 6 oz glass of water or juice for administration. What volume of the KCl 10% liquid should be used for Mrs. Turner s usual daily dose? Multiply the desired dose by the concentration. 1. Multiply the desired dose by the concentration. 10 meq x 15 ml = 7.5 ml of KCl 10% liquid day 20 meq day Number: 7.5 Units: ml / day

6 6. Problem type: IV flow + allergic reaction Medication: ceftriaxone hypothetical PROBLEM Mrs. Turner s original orders called for ceftriaxone, 1g, to be administered intravenously daily. The solution has been diluted to a concentration of 1 g / 50 ml to be administered over 30 minutes. Twenty minutes into the first infusion, Mrs. Turner reports an adverse reaction to the antibiotic and the infusion is stopped. How many ml of concentration were administered before the infusion was stopped? Round your answer to the nearest whole number. Divide the time elapsed by the infusion rate to determine the completion percentage of the infusion. 1. Determine the completion percentage of the infusion. 20 min (time elapsed) = (or 66.7 %) 30 min (total infusion time) 2. Multiply the infusion volume by the percentage. 50 ml x = X X = 33 ml Number: 33 Units: ml

7 7. Problem type: Dosage calculation + weight based dosage Medication: hospital hypothetical According to the Davis s Drug Guide, children six months old or younger with community acquired pneumonia can be administered azithromycin orally using a weight based dosage. Children in this age group can receive 10 mg/kg on the first day, then 5 mg/kg for four more days. Assume you need to administer this to a child weighing 20.3 lbs. What is the total dose of azithromycin the child will receive over five days? Round your answer to the nearest whole number. Convert pounds to kilograms, and multiply the weight by the dosage. 1. Convert pounds (lbs) to kilograms (kg) lbs x 1 kg = kg 2.20 lb 2. Multiply the first day s dosage by weight in kg. 10 mg x kg = mg kg 3. Multiply the dosage given for days 2 5 by weight in kg, and multiply by the number of days administered (4) kg x 5 mg x 4 = mg kg 4. Add the results from steps 2 and mg mg = mg, rounded to 277 mg Number: 277 mg Units: mg

8 8. Problem type: Unit conversation + stock on hand Medication: hospital Mrs. Turner s orders called for 50 mcg of levothyroxine, by mouth, daily. The pharmacy stocks the medication in mg tablets. How many tablets are needed to administer the ordered dose? Start by converting 50 mcg to mg. Then use the equation below, where X is the number of tablets that should be administered. D (ordered dose ) x Quantity = X H (dose on hand) 1. Convert micrograms (mcg) to milligrams (mg). 50 mcg x 1 mg = 0.05 mg 1000 mcg 2. Determine what information you have. D = 0.05 mg H = mg Q = 1 tablet 3. Plug into the equation and solve. Number: 2 Units: tablets D (0.05 mg) x 1 tablet = X H (0.025 mg) X = 2 tablets

9 9. Problem type: Total daily dose calculation Medication: Units of home At home, Mrs. Turner takes 16 units of insulin aspart, twice a day with meals. She also takes 45 units of long acting insulin glargine, daily. How many total units of insulin does Mrs. Turner take daily? Start by multiplying the dosage of insulin aspart by how often Mrs. Turner takes it. 1. Multiply the dosage by the number of units per dose. 16 units x 2 = 32 units 2. Add the total number of insulin aspart units and the total number of insulin glargine units. Number: 77 Units: units 32 units + 45 units = 77 units

10 10. Problem type: Dosage calculation Medication: Insulin hospital hypothetical The provider ordered insulin aspart on a sliding scale for 1 unit/10 g CHO subcutaneous + 1 unit/50 points above 150 BG. Mrs. Turner will eat a meal that contains 40 g CHO and has a pre meal BG level of 160. How many units of insulin should be administered? Add the units calculated from the sliding scale to the units necessary for the patient s current BG level. 1. Perform the sliding scale calculation (1 unit/10g CHO). 40 g CHO x 1 unit = 4 units 10 g CHO 2. Subtract 150 from Mrs. Turner s pre meal BG. 160 BG 150 BG = 10 points 3. Multiply 10 points by the number of units per 50 points. 10 points x 1 unit = 0.2 units 50 points Round down to the next whole unit = 0 unit 4. Add the units from the sliding scale to the additional units needed for every 50 points above 150 BG. 4 units + 0 unit = 4 units Number: 4 Units: units

11 11. Problem type: Unit conversion + orders correction Medication: hospital hypothetical Suppose Mrs. Turner s provider writes a revised order of 25 mg of her daily levothyroxine. Given that her original order was in micrograms, you suspect this new order contains an error. You take the appropriate measures to get the orders corrected in order to avoid administering an overdose. If the error had not been caught, how many times more levothyroxine would have been given? Start by converting 25 mg to micrograms. 1. Convert milligrams (mg) to micrograms (mcg). 25 mg x 1000 mcg = 25,000 mcg 1 mg 2. Divide the incorrect mcg dosage by correct mcg dosage. 25,000 mcg = mcg Number: 1000 Units: times overdose

12 12. Problem type: IV flow rate + drop factor Medication: hospital hypothetical Suppose Mrs. Turner s provider orders 500 mg of azithromycin to be delivered in a 250 ml IV solution over 3 hours. The dose will be delivered using IV tubing with a drop factor of 15 (15 gtt (drops) = 1 ml) What is the appropriate rate of flow for the IV, in drops per minute? Round your answer to the nearest whole number. Start by determining how many ml will be delivered per minute. 1. Divide the total number of ml needed to deliver the 500 mg dilution by the expected duration in minutes, converting hours to minutes. 250 ml x 1 hr = ml/min 3 hr 60 min 2. Multiply the ml / min by the drop factor and round to the nearest whole number ml x 15 gtt = 20.8 gtt/min 1 min 1 ml 3. Round your answer to the nearest whole number. = 21 gtt / min Number: 21 Units: gtt / min

13 13. Problem type: IV flow rate + drop factor Medication: hospital hypothetical On the second day of hospitalization, Mrs. Turner s orders call for 500 mg of azithromycin to be delivered in a 250 ml IV solution over 3 hours. The dose will be delivered using IV tubing with a drop factor of 10 (10 gtt (drops) = 1 ml). What is the appropriate rate of flow for the IV in drops per minute? Round your answer to the nearest whole number. Start by determining how many ml will be delivered per minute. 1. Divide the total number of ml needed to deliver the 500 mg dilution by the expected duration, converting hours to minutes. 250 ml x 1 hr = ml/min 3 hr 60 min 2. Multiply the ml / min by the drop factor and round to the nearest whole number ml x 10 gtt = gtt / min 1 min 1 ml Number: 14 Units: gtt / min Round your answer to the nearest whole number = 14 gtt / min

14 14. Problem type: Correct days supply Medication: primary care hypothetical Mrs. Turner is prescribed insulin aspart, 16 units, SC TID at mealtimes. When Mrs. Turner returns home, the provider would like to switch her meal time insulin administration to a pen delivery device instead of insulin syringes. The provider will keep the same dose. Assume that Mrs. Turner eats three meals a day. If the pen cartridges contain 3 ml of U 100 insulin aspart, how often will Doris need to replace the cartridge? Round your answer down to the nearest whole day. U 100 insulin contains 100 units / 1 ml. 1. Multiply the number of units by the number of meals each day. 16 units x 3 meals = 48 units of insulin aspart meal day day 2. Multiply the concentration of U 100 insulin by the volume of a cartridge. 100 units x 3 ml = 300 units ml cartridge cartridge 3. Multiply the result from step 2 by the number of units per day, so that the units cancel. Number: 6 Units: days 300 units x 1 day = 6.25 days / cartridge, rounded to 6 days cartridge 48 units

15 15. Problem type: Correct days supply Medication: primary care hypothetical Assume that Mrs.Turner s provider decides to prescribe insulin aspart, 16 units SC TID at mealtimes, and Mrs. Turner receives a U 100, 10 ml vial of insulin aspart. Assume that Mrs. Turner eats three meals a day. How long would a U 100, 10 ml vial of insulin aspart last at this dosage? Round your down answer to the nearest whole day. U 100 insulin contains 100 units / 1 ml. 1. Multiply the number of units by the number of meals each day. 16 units x 3 meals = 48 units of insulin aspart meal day day 2. Multiply the concentration of U 100 insulin by the volume of the vial. 100 units x 10 ml = 1000 units 1 ml vial vial 3. Multiply the result from step 2 by the number of units per day, so that the units cancel. Number: 20 Units: days 1000 units x 1 day = 20.8 days/vial, rounded down to 20 days Vial 48 units

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