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On Greg's last visit to his doctor, he complained of feeling tired. His doctor orders a blood test for iron. Sandra, the registered nurse, does a venipuncture and withdraws \(8.0 \mathrm{~mL}\) of blood. About \(70 \%\) of the iron in the body is used to form hemoglobin, which is a protein in the red blood cells that carries oxygen to the cells of the body. About \(30 \%\) is stored in ferritin, bone marrow, and the liver. When the iron level is low, a person may have fatigue and decreased immunity. The normal range for serum iron in men is 80 to \(160 \mathrm{mcg} / \mathrm{dL}\). Greg's iron test showed a blood serum iron level of \(42 \mathrm{mcg} / \mathrm{dL}\), which indicates that Greg has iron deficiency anemia. His doctor orders an iron supplement to be taken twice daily. One tablet of the iron supplement contains \(65 \mathrm{mg}\) of iron. $ a. Write an equality and two conversion factors for one tablet of the iron supplement. b. How many grams of iron will Greg consume in one week?

Step by step solution

01

Understanding the Problem

Greg is diagnosed with iron deficiency anemia and is prescribed an iron supplement to be taken twice daily. The aim is to find out how many grams of iron Greg will consume in one week.

02

Write an Equality

One tablet of the iron supplement contains 65 mg of iron. The equality can be written as: 1 tablet = 65 mg of iron.

03

Identify the Conversion Factors

Two conversion factors can be derived from the given equality: 1. \( \frac{65 \mathrm{mg}}{1 \text{tablet}} \)2. \( \frac{1 \text{tablet}}{65 \mathrm{mg}} \)

04

Calculate the Iron Consumed Daily

Since Greg takes 2 tablets a day, the daily iron consumption is:\( 2 \text{tablets} \times 65 \mathrm{mg/tablet} = 130 \mathrm{mg} \)

05

Convert Milligrams to Grams

To convert the daily iron consumption from mg to g, use the conversion factor \( 1 \mathrm{g} = 1000 \mathrm{mg} \):\( 130 \mathrm{mg} \times \frac{1 \mathrm{g}}{1000 \mathrm{mg}} = 0.13 \mathrm{g} \)

06

Calculate Weekly Consumption

Multiply the daily iron consumption in grams by 7 (the number of days in a week):\( 0.13 \mathrm{g/day} \times 7 \text{days} = 0.91 \mathrm{g} \)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

hemoglobin

Hemoglobin is a protein in red blood cells responsible for transporting oxygen throughout the body. Each red blood cell is packed with thousands of hemoglobin molecules. Hemoglobin binds to oxygen in the lungs and releases it in tissues and organs where it's needed.
In the context of Greg's condition, roughly 70% of the body's iron is bound within hemoglobin. This is essential because iron is a key component of hemoglobin, enabling it to bind and carry oxygen. Low iron levels can thus lead to inadequate oxygen delivery to cells, causing fatigue, which is one of Greg's main complaints. Iron deficiency can reduce hemoglobin production, leading to iron deficiency anemia, the condition Greg was diagnosed with.

conversion factors

Conversion factors are essential in transforming one unit of measurement into another. They are often expressed as fractions that equal one.
In Greg's case, the equality is: 1 tablet = 65 mg of iron. From this, we can derive two conversion factors:
- \(\frac{65 \text{ mg}}{1 \text{ tablet}}\)
- \(\frac{1 \text{ tablet}}{65 \text{ mg}}\)
Using these conversion factors, you can easily translate between tablets and milligrams. This is particularly useful in medical contexts where dosages must be accurately understood and applied.

iron supplements

Iron supplements are prescribed to restore adequate levels of iron in the body. These supplements are especially important in treating conditions like iron deficiency anemia.
For Greg, his doctor recommended taking an iron supplement twice daily, each containing 65 mg of iron. This consistent dosage helps boost his low iron levels and, by extension, increases his hemoglobin production. Correct dosage adherence ensures that Greg's condition improves safely and effectively.
Always follow the prescribed dosage and consult with a healthcare professional before making any changes.

milligrams to grams conversion

Understanding unit conversions is crucial in various scientific and everyday contexts. One common conversion is from milligrams (mg) to grams (g).
The conversion factor between milligrams and grams is:\[1 \text{ g} = 1000 \text{ mg}\]
To convert milligrams to grams, divide the mass in milligrams by 1000. For instance, Greg's daily iron intake from two tablets is 130 mg. To convert this to grams, you use the formula:\[130 \text{ mg} \times \frac{1 \text{ g}}{1000 \text{ mg}} = 0.13 \text{ g}\]
Over a week, Greg consumes:\[0.13 \text{ g/day} \times 7 \text{ days} = 0.91 \text{ g}\]
This helps quantify his weekly iron intake in more familiar units.