Working in the health sciences, you will find that you will have to make different kinds of mathematical conversions. Start this activity by reading through the following story problems to familiarize yourself with the various conversions that you will need to perform. Then, go online and research measurement conversions, collecting information that will help you make the appropriate conversions in the story problems below. Submit all of your work including any conversion charts or information that you used to complete the story problems.

A patient is prescribed 80 mg of Tramadol Hydrochloride injection. The stock dose is 50mg / 2 mL. What volume will you require?
A laboratory technician measures 48 ml of urine sample in a 4-ounce beaker. How many more ml of urine are necessary to fill the beaker?
You fill a storage cabinet with 12 bottles of normal saline. Each bottle contains 1000 mL. How many ounces of this solution are in the storage cabinet?
A patient is prescribed 6 mg of cough medication. The label on the prescription says there are 2 mg per 4 mL. How many teaspoons of cough medication does the patient need to take?
A patient requires 80 milligrams of Risperidone. The stock dose is 40mg / 10mL. What volume is required?
Normal urinary output for an adult is between 400 to 2,000 mL daily. If a person follows the recommended 8 glasses of 8 ounces of liquid intake and has an output of 1,500 mL, what is their net liquid gain / loss?
Dymelor 0.75 g is ordered. Scored tablets are labeled 500 mg. each. How many tablets will you give?

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Math Conversions Student submits answers to all math problems with clear work that shows conversions made. Student submits answers and all work, but explanations or work may not be fully clear. Student does not submit all answers, and / or does not submit work along with the answers.

1 answer

To solve the problems stated, we'll perform the necessary mathematical conversions step by step. Below is a breakdown of each problem, along with the conversions performed and the final answers.

Conversion Reference Information

  1. Milligrams to Milliliters: If given concentration, use the ratio to convert.
  2. Ounces to Milliliters: 1 ounce = 29.5735 mL (for practical purposes, use 30 mL).
  3. Teaspoons to Milliliters: 1 teaspoon = 5 mL.
  4. Grams to Milligrams: 1 g = 1000 mg.

Problem 1

A patient is prescribed 80 mg of Tramadol Hydrochloride injection. The stock dose is 50 mg / 2 mL. What volume will you require?

Solution:

  • From the stock dose: 50 mg in 2 mL implies: \[ \frac{50 , \text{mg}}{2 , \text{mL}} = 25 , \text{mg/mL} \]
  • To find the volume required for 80 mg: \[ \text{Volume} = \frac{\text{Desired dose}}{\text{Concentration}} = \frac{80 , \text{mg}}{25 , \text{mg/mL}} = 3.2 , \text{mL} \]

Problem 2

A laboratory technician measures 48 ml of urine sample in a 4-ounce beaker. How many more ml of urine are necessary to fill the beaker?

Solution:

  • Convert ounces to mL: \[ 4 , \text{oz} \times 30 , \text{mL/oz} = 120 , \text{mL} \]
  • Calculate remaining volume: \[ \text{Volume needed} = 120 , \text{mL} - 48 , \text{mL} = 72 , \text{mL} \]

Problem 3

You fill a storage cabinet with 12 bottles of normal saline. Each bottle contains 1000 mL. How many ounces of this solution are in the storage cabinet?

Solution:

  • Total volume in mL: \[ 12 , \text{bottles} \times 1000 , \text{mL/bottle} = 12000 , \text{mL} \]
  • Convert mL to ounces: \[ \frac{12000 , \text{mL}}{30 , \text{mL/oz}} \approx 400 , \text{oz} \]

Problem 4

A patient is prescribed 6 mg of cough medication. The label on the prescription says there are 2 mg per 4 mL. How many teaspoons of cough medication does the patient need to take?

Solution:

  • Calculate required volume for 6 mg: \[ 2 , \text{mg} \text{ in } 4 , \text{mL} \implies \frac{6 , \text{mg}}{2 , \text{mg}} \times 4 , \text{mL} = 12 , \text{mL} \]
  • Convert mL to teaspoons: \[ \frac{12 , \text{mL}}{5 , \text{mL/teaspoon}} = 2.4 \text{ teaspoons} \]

Problem 5

A patient requires 80 milligrams of Risperidone. The stock dose is 40 mg / 10 mL. What volume is required?

Solution:

  • From the stock dose: \[ \frac{40 , \text{mg}}{10 , \text{mL}} = 4 , \text{mg/mL} \]
  • To find the volume needed for 80 mg: \[ \text{Volume} = \frac{80 , \text{mg}}{4 , \text{mg/mL}} = 20 , \text{mL} \]

Problem 6

Normal urinary output for an adult is between 400 to 2,000 mL daily. If a person follows the recommended 8 glasses of 8 ounces of liquid intake and has an output of 1,500 mL, what is their net liquid gain/loss?

Solution:

  • Total liquid intake: \[ 8 , \text{glasses} \times 8 , \text{oz/glass} \times 30 , \text{mL/oz} = 1920 , \text{mL} \]
  • Calculate net gain/loss: \[ \text{Net} = 1920 , \text{mL} - 1500 , \text{mL} = 420 , \text{mL gain} \]

Problem 7

Dymelor 0.75 g is ordered. Scored tablets are labeled 500 mg each. How many tablets will you give?

Solution:

  • Convert grams to milligrams: \[ 0.75 , \text{g} = 750 , \text{mg} \]
  • Calculate number of tablets: \[ \text{Tablets required} = \frac{750 , \text{mg}}{500 , \text{mg/tablet}} = 1.5 , \text{tablets} \] (The patient may need 1.5 tablets, depending on the form of administration.)

Summary of Answers:

  1. 3.2 mL
  2. 72 mL
  3. 400 oz
  4. 2.4 teaspoons
  5. 20 mL
  6. 420 mL gain
  7. 1.5 tablets

Feel free to generate and attach any additional conversion charts for full documentation of all conversions.