Math Practice for Paramedic Students: Calculating Medication Dosages for Etomidate and Succinylcholine.

Problem 1: Etomidate Dose Calculation

#### Given:
- Patient weight: 175 pounds
- Dose required: 0.3 mg/kg of etomidate
- Etomidate vial concentration: 2 mg/mL

#### Steps to Solve:

1. Convert patient weight from pounds to kilograms:
- 1 pound = 0.4536 kg
- Patient weight in kg = \( 175 \times 0.4536 \)
\[
175 \times 0.4536 = 79.38 \, \text{kg}
\]

2. Calculate the total dose of etomidate required:
- Dose per kg = 0.3 mg/kg
- Total dose = \( 79.38 \, \text{kg} \times 0.3 \, \text{mg/kg} \)
\[
79.38 \times 0.3 = 23.814 \, \text{mg}
\]

3. Determine the volume of etomidate to draw up:
- Concentration of etomidate = 2 mg/mL
- Volume required = \( \frac{\text{Total dose}}{\text{Concentration}} \)
\[
\frac{23.814 \, \text{mg}}{2 \, \text{mg/mL}} = 11.907 \, \text{mL}
\]

4. Determine the number of vials required:
- Each vial contains 20 mg of etomidate.
- Number of vials = \( \frac{\text{Total dose}}{\text{Dose per vial}} \)
\[
\frac{23.814 \, \text{mg}}{20 \, \text{mg/vial}} = 1.1907 \, \text{vials}
\]
Since you cannot use a fraction of a vial, you will need 2 vials.

#### Final Answers for Problem 1:
- Total dose required: \( \boxed{23.81 \, \text{mg}} \)
- Volume to draw up: \( \boxed{11.91 \, \text{mL}} \)
- Number of vials required: \( \boxed{2} \)

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Problem 2: Succinylcholine Dose Calculation

#### Given:
- Patient weight: 175 pounds
- Dose required: 1.5 mg/kg of succinylcholine
- Succinylcholine vial concentration: 20 mg/mL

#### Steps to Solve:

1. Convert patient weight from pounds to kilograms:
- 1 pound = 0.4536 kg
- Patient weight in kg = \( 175 \times 0.4536 \)
\[
175 \times 0.4536 = 79.38 \, \text{kg}
\]

2. Calculate the total dose of succinylcholine required:
- Dose per kg = 1.5 mg/kg
- Total dose = \( 79.38 \, \text{kg} \times 1.5 \, \text{mg/kg} \)
\[
79.38 \times 1.5 = 119.07 \, \text{mg}
\]

3. Determine the volume of succinylcholine to draw up:
- Concentration of succinylcholine = 20 mg/mL
- Volume required = \( \frac{\text{Total dose}}{\text{Concentration}} \)
\[
\frac{119.07 \, \text{mg}}{20 \, \text{mg/mL}} = 5.9535 \, \text{mL}
\]

#### Final Answer for Problem 2:
- Total dose required: \( \boxed{119.07 \, \text{mg}} \)
- Volume to draw up: \( \boxed{5.95 \, \text{mL}} \)

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Summary of Final Answers:

1. Etomidate:
- Total dose: \( \boxed{23.81 \, \text{mg}} \)
- Volume: \( \boxed{11.91 \, \text{mL}} \)
- Vials: \( \boxed{2} \)

2. Succinylcholine:
- Total dose: \( \boxed{119.07 \, \text{mg}} \)
- Volume: \( \boxed{5.95 \, \text{mL}} \)