Calculations I: Math Basics

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26 Terms

1

LF is a 3-year-old boy who presents to the pediatrician's office with his mother. He has been complaining of ear pain and has had a fever up to 101ºF. He is 96 cm tall and weighs 36 lb. The pediatrician prescribes amoxicillin 80 mg/kg/day, divided in two doses. How many milliliters of the 400 mg/5 mL solution should he receive for each dose? (Answer must be numeric; no units or commas; round the final answer to the nearest TENTH.)

8.2 mL

The patient requires 40 mg/kg/dose x 16.3636 kg = 654.5454 mg

654.5454 mg x 5 mL/400 mg = 8.18 mL rounded to 8.2 mL per dose.

p. 128

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2

A 10 gram packet of potassium chloride provides 20 mEq of potassium. How many grams of powder would provide 9 mEq of potassium? (Answer must be numeric; no units or commas; round the final answer to the nearest TENTH.)

4.5 g

p. 126

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3

An order is written for IV cyclosporine 5 mg/kg. How many milliliters of a 50 mL bag containing 100 mg of cyclosporine per milliliter should be administered to a 165 pound liver transplant patient? (Answer must be numeric; no units or commas; round the final answer to the nearest TWO DECIMAL PLACES.)

3.75 mL

The cyclosporine concentration is 100 mg/mL (not 100 mg/50 mL). Be sure to read each question carefully.

p. 126

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4

How many milliliters of guaifenesin syrup are contained in each dose of the prescription below? (Answer must be numeric; no units or commas; round the final answer to the nearest WHOLE number.)

Rx:

Phenergan syrup 60 mL

Guaifenesin syrup qs ad 200 mL

Sig. ii tsp PRN cough

7 mL

200 mL total - 60 mL Phenergan = 140 mL guaifenesin

140 mL guaifenesin/200 mL Rx = X mL guaifenesin / 10 mL Rx dose

X = 7 mL guaifenesin per dose

p. 128

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5

An albuterol metered dose inhaler (MDI) provides 90 mcg of medication in each inhalation. If the total weight of the medication in the canister is 18 mg, how many inhalations will be required to deplete the MDI? (Answer must be numeric; no units or commas; round the final answer to the nearest WHOLE number.)

200 inhalations

18 mg x 1,000 mcg/mg = 18,000 mcg of medication are contained in the canister.

p. 127

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6

A 30 mL nasal spray delivers 18 sprays per mL of solution. Each spray contains 1.25 mg of active drug. How many milligrams of the active drug does the 30 mL nasal spray contain? (Answer must be numeric; no units or commas; round the final answer to the nearest WHOLE number.)

675 mg

This is easily solved with dimensional analysis: 1.25 mg/spray x 18 sprays/1 mL x 30 mL = 675 mg

p. 126

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7

Calculate the body mass index (BMI) for a patient who is 6'2' and weighs 198 pounds. Use the formula provided below. (Answer must be numeric; no units or commas; round the final answer to the nearest WHOLE number.)

BMI (kg/m2) = weight in pounds/(height in inches)^2 x 703

25

The formula for BMI is provided in the question but must be memorized for the exam. A BMI between 25 and 29.9 kg/m is considered overweight. This is reviewed in more detail in the Calculations IV chapter.

p. 134

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8

TW takes furosemide 80 mg PO BID at home. His prescriber would like to switch him to oral bumetanide once daily. What is the equivalent oral dose of bumetanide? Oral furosemide 40 mg = oral bumetanide 1 mg. (Answer must be numeric; no units or commas; round the final answer to the nearest WHOLE number.)

4 mg

The patient currently takes 160 mg of furosemide per day. 160 mg furosemide/X mg bumetanide = 40 mg furosemide/1 mg bumetanide. The conversion between furosemide and bumetanide is provided in this question but must be memorized for the exam.

p. 133

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9

How many milliliters of aminophylline injection (250 mg aminophylline/10 mL) should be used in filling a medication order calling for 10 mg of aminophylline? (Answer must be numeric; no units or commas; include a leading zero when the answer is <1; round the final answer to the nearest TENTH.)

0.4 mL

250 mg/10 mL = 10 mg/X mL

p. 126

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10

The pharmacist receives a prescription for "Cefaclor 500 mg #30, Sig: i cap po q 8 hrs." How many days will this prescription last if the patient takes it as directed?

A. 3

B. 5

C. 30

D. 10

E. 15

D. 10

The patient should be instructed to take one capsule by mouth every 8 hours.

p. 128

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11

If one 10 mL vial contains 0.05 g of diltiazem, how many milliliters should be administered to provide a 150 mg dose of diltiazem? (Answer must be numeric; no units or commas; round the final answer to the nearest WHOLE number.)

30 mL

Units must match when using proportions.

10 mL/0.05 g = X mL/0.15 g

p. 126

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12

If a codeine suspension contains 15 mg of codeine per 5 mL, how many grams of codeine would be used in preparing 240 mL of the suspension? (Answer must be numeric; no units or commas; include a leading zero when the answer is less than 1; round the final answer to the nearest HUNDREDTH.)

0.72 g

15 mg/5mL = X mg/240 mL; X = 720 mg or 0.72 grams

p. 126

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13

The intravenous dose of digoxin is 80% of the oral digoxin dose. If the oral dose is 20 mcg/kg, what is the intravenous dose, in micrograms, for a 6-year-old child weighing 50 lbs? (Answer must be numeric; no units or commas; round the final answer to the nearest WHOLE number.)

364 mcg

50 lbs x 1 kg/2.2 lbs x 20 mcg/kg x 0.8 = 363.6363, round to 364

p. 134

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14

How many grains of aspirin will each capsule contain? (Answer must be numeric; no units or commas; round the final answer to the nearest ONE DECIMAL PLACE.)

Aspirin 15 g

Diphenhydramine 1.2 g

Lactose 1 g

No. 30 caps

Sig: One capsule QHS PRN sleep

7.7 grains

1 grain = 65 mg

15 g x 1000 mg/1 g = 15,000 mg

15,000 mg x 1 grain/65 mg = 230.76 grain

230.76 grain/30 capsules = 7.692 or 7.7 grain/capsule

p. 125

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15

JF is a 72-year-old man who weighs 208 pounds. Calculate his weight in kilograms. (Answer must be numeric; no units or commas; round the final answer to the nearest TENTH.)

94.5 kg

The weight in kilograms is 94.545454, which rounds to 94.5 per the instructions in the question. Rounding should only be performed once - on the last step of multi-step calculations.

p. 125

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16

If 150 capsules contain 400 mg of an active ingredient, how many milligrams of the active ingredient will 84 capsules contain? (Answer must be numeric; no units or commas; round the final answer to the nearest WHOLE number.)

224 mg

150 capsules/400 mg = 84 capsules/x mg

p. 126

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17

MK takes OTC ferrous gluconate 324 mg PO TID. If ferrous gluconate contains 12% elemental iron, how many milligrams of elemental iron does MK receive daily? (Answer must be numeric; no units or commas; round the final answer to the nearest WHOLE number.)

117 mg

Elemental iron composition for common products is also reviewed in the Anemia chapter. Common drug conversions that must be memorized for NAPLEX are listed on the Required Formulas Sheet in the RxPrep Course Book.

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18

A compounding pharmacist receives a prescription for ninety 60 mcg levothyroxine (T4) capsules. He has 150 mcg tablets in stock and will use these to prepare the capsules. How many tablets will he need to fill this prescription? (Answer must be numeric; no units or commas, round the final answer to the nearest WHOLE number.)

36 tablets

p. 128

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19

A pharmacist received this prescription:

Erythromycin Ethylsuccinate 200 mg/5 mL

Sig: 5 mL PO TID x 10 days

The pharmacist dispensed 4 ounces to the patient. How many days of therapy will the patient be short?

A. 4 days

B. 5 days

C. The patient will have exactly enough medication to complete 10 days of therapy.

D. 1 day

E. 2 days

E. 2 days

The patient needs 150 mL to complete the course of therapy. 150 mL - 120 mL (quantity dispensed) = 30 mL short. Notice that the question asks how many days of therapy, the patient will be short. 30 mL = 2 days short.

p. 128

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20

The pharmacist receives a prescription for "Percocet 5/325 mg tab #24, Sig; i-ii tabs po q 4-6 hrs prn pain x 2 days." According to the instructions on the prescription, what is the maximum number of tablets that the patient can take in one day?

A. 12

B. 8

C. 24

D. 6

E. 4

A. 12

p. 128

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21

A patient weighs 278 pounds. What is the formula to convert the patient's weight to kilograms?

A. Multiply the weight in pounds by 2.2

B. Divide the weight in pounds by 2.2

C. Multiply the weight in pounds by 0.85

D. Multiply the weight in pounds by 2.54

E. Divide the weight in pounds by 2.54

B. Divide the weight in pounds by 2.2

p. 125

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22

The pharmacist receives this prescription:

Acetaminophen 12 g

Aspirin 12 g

Caffeine 3.12 g

M. ft. caps. no. 48

Sig: i-ii capsules PRN HA

How many milligrams of caffeine will each capsule contain? (Answer must be numeric; no units or commas; round the final answer to the nearest WHOLE number.)

65 mg

Review Common Medical Abbreviations in the Quick Guides section of the RxPrep Course Book. "M. ft." means "mix and make" - as in "mix all of the ingredients and make 48 capsules" in this case.

3120 mg of caffeine/48 capsules = X mg/1 capsule

p. 128

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23

Oral potassium chloride 10% solution contains 20 mEq of potassium per 15 mL of solution. A patient is prescribed 22 mEq of potassium daily. How many milliliters of potassium chloride 10% will the patient receive each day? (Answer must be numeric; no units or commas; round the final answer to the nearest TENTH.)

16.5 mL

This question is solved with a simple one-step proportion (22 mEq/X mL = 20 mEq/15 mL), though it might initially look more difficult.

p. 126

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24

A pharmacist receives an order for voriconazole 6 mg/kg IVPB Q12H x 24 hours for a patient weighing 150 lbs. How many milligrams of voriconazole will the patient receive in total? (Answer must be numeric; no units or commas; round the final answer to the nearest WHOLE number.)

818 mg

p. 128

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25

How many milliliters of Mylanta suspension are contained in each dose of the prescription below?

Belladonna Tincture 30 mL

Phenobarbital 70 mL

Mylanta susp. qs. ad 200 mL

Sig 20 mL BID

10 mL

200 mL - 30 mL - 70 mL = 100 mL of Mylanta suspension

100 mL of mylanta/200 total = X Mylanta/20 mL per dose

X = 10 mL

p. 128

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26

RS is admitted to the hospital. His medication orders are as follows:

2/18:

D/C IV fluid from 2/17

D/C KCl PO

NS 1 liter +

7 mEq Ca gluconate at 40 mL/hr

Norvasc 10 mg PO daily

Protonix 40 mg daily

Lovenox 40 mg daily

Atenolol 100 mg PO daily

The pharmacist has 10% calcium gluconate vials that are labeled to contain 0.465 mEq/mL. How many milliliters of calcium gluconate are required to prepare the fluid ordered on February 18th?

(Answer must be numeric; no units or commas; round the final answer to the nearest WHOLE number.)

15 mL

The order calls for 7 mEq of calcium gluconate. 7 mEq x 1 mL / 0.465 mEq = 15 mL of 10% calcium gluconate

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