8.7.2: Exercise 3.1-C Acetaminophen Overdoses

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MAKING CONNECTIONS TO THE COLLABORATION

(1) Which of the following was one of the main mathematical ideas of the collaboration?

(i) Units can be used to set up conversion problems by using the fact that common factors in the numerator and denominator of a fraction divide out to one.

(ii) The confusion about different concentrations of acetaminophen can result in dangerous consequences.

(iii) Units can be used to set up conversion problems by using the fact that common factors in the numerator and denominator of a fraction can be subtracted to equal zero.

(iv) It is possible to convert milligrams per milliliter into grams per liter.

DEVELOPING SKILLS AND UNDERSTANDING

(2) Use Figure 1 for the following questions.

Figure 1

$8.7.2 figure.PNG$

(a) (i) What fraction of Figure 1 is shaded?

(ii) Shade the same fraction of the area in Figures 2 and 3.

Figure 2

$8.7.2 figure b.PNG$

Figure 3

$8.7.2 figure c.PNG$

(b) How many boxes did you shade for Figure 2?

(3) You are a pediatric medical assistant. You have a patient who is six months old. Your patient has a fever of 102.5 degrees Fahrenheit. The pediatric doctor prescribes a dose of 2.5 mL of acetaminophen solution to help lower fever. The doctor does not specify which formula to use: children’s or infants’ formula.

Use dimensional analysis to determine which formula to use based on the doctor’s prescription.

(a) Children’s concentration is 160mg/5 mL. The doctor prescribes 2.5 mL.

This gives you _________ mg.

(b) Infants’ concentration is 80mg/1mL. The doctor prescribes 2.5 mL.

This gives you _________ mg.

(d) Explain to the patient’s parents what formula to use and why they need to be cautious about the type of formula they give their infant. (Write an explanation of 2–3 sentences.)

(4) You are working as a medical assistant in a clinic. You are in charge of restocking the office supply of acetaminophen. There are 160 mg of acetaminophen in 5 mL. You are ordering 2 L of acetaminophen. How many grams (g) of acetaminophen will you have available to give to patients? Use dimensional analysis to determine this. Remember 1,000 milligrams (mg) = 1 gram.

Other Applications of Dimensional Analysis

Dimensional analysis can be used in many different applications, not just calculating medicine dosages. In the following questions, you will be applying the method you learned in Collaboration 3.1 to other situations. Here are some helpful conversions: 60 seconds = 1 minute, 60 minutes = 1 hour, 1 meter = 3.28 feet, 5,280 feet = 1 mile.

(5) Nurses are often required to calculate dosages. That is, they must check the order that a doctor has given for the administration of a drug and decide whether the dosage is correct. To calculate correctly they must convert between different metric units. For example, 1,000 milligrams (mg) = 1 gram.

(a) Suppose a doctor has ordered a dose of 0.1 g of a medication. The drug comes in a solution concentration of 200 mg per 1 mL. How many milliliters of this solution is required?

(b) Suppose a doctor has ordered a dose of 3 g of a medication. The drug comes in a solution concentration of 300 mg per 1 ml. How many teaspoons of the solution is required?

(6) A 2014 Toyota Prius hybrid vehicle gets 48 mpg for highway driving. The tank holds 11.9 gallons of fuel.³ Typically the low fuel warning light comes on when approximately two gallons of fuel remain in the tank. Which of the following calculations can be used to find the distance that can be traveled after the fuel light comes on and before the car runs out of gasoline?

(i) $\dfrac{1}{2\;gallons}\cdot \dfrac{48\;miles}{1\;gallon} = 24\;miles$

(ii) $\dfrac{2\;gallons}{1}\cdot \dfrac{48\;miles}{1\;gallon} = 96\;miles$

(iii) $\dfrac{11.9\;gallons}{1}\cdot \dfrac{48\;miles}{1\;gallon} = 571.2\;miles$

(iv) $\dfrac{2\;gallons}{1}\cdot \dfrac{1\;gallon}{48\;miles} = \dfrac{1}{24} miles$

MAKING CONNECTIONS ACROSS THE COURSE

(8) In Collaboration 1.6, you learned about a water footprint. Part of a person’s water footprint is the water used for cleaning. In this question, you will calculate the cost of water for laundry and bathing. You will use the City of New York 2014 rate of $9.27/100 cubic feet of water. Calculate the cost of each of the following based on this rate. Use the conversion factor of 7.48 gallons per cubic foot. ⁴

(a) A standard washing machine uses approximately 50 gallons of water per load.⁵ A household washes one load of laundry per week for 52 weeks. Find the total cost per year. Round to the nearest dollar per year.

(b) According to one study, the average American shower lasts for 8.2 minutes and uses 17.2 gallons of water.⁶ A person showers once a day for a year. Find the total cost per year. Round to the nearest dollar per year.

_____________________________________

³ http://www.toyota.com/prius/features.html#!/weights_capacities/1223/1225/1227/1229

⁴ http://www.nyc.gov/html/dep/html/residents/wateruse.shtml

⁵ ibid.

⁶ ibid.

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