Problem 44 - Calculus for Biology and Medicine

Question

(a) To convert the weight of an object from kilograms (kg) to pounds (lb), you use the facts that a weight measured in kilograms is proportional to a weight measured in pounds and that 1 kg corresponds to \(2.20 \mathrm{lb} .\) Find an equation that relates weight measured in kilograms to weight measured in pounds. (b) Use your answer in (a) to convert the following measurements: (i) \(63 \mathrm{lb}\) (ii) \(150 \mathrm{lb}\) (iii) \(2.5 \mathrm{~kg}\) (iv) \(140 \mathrm{~kg}\)

Step-by-Step Solution

Answer

For (a): Pounds = Kilograms × 2.20; Kilograms = Pounds × 0.4545. For (b): (i) 28.626 kg, (ii) 68.175 kg, (iii) 5.5 lb, (iv) 308 lb.

Step 1: Understand the Proportional Relationship

The problem indicates that weight in kilograms is proportional to weight in pounds. This means that there is a constant conversion factor between the two units.

Step 2: Identify the Conversion Factor

According to the problem, 1 kg is equivalent to 2.20 lb. This means that the conversion factor from kg to lb is 2.20. Conversely, the conversion factor from lb to kg is the reciprocal, which is \( \frac{1}{2.20} \approx 0.4545 \).

Step 3: Establish the Conversion Equations

From Step 2, we get two equations:Converting kilograms to pounds: \[ \text{Pounds} = \text{Kilograms} \times 2.20 \]Converting pounds to kilograms: \[ \text{Kilograms} = \text{Pounds} \times 0.4545 \]

Step 4: Convert the Given Measurements

Using the equations from Step 3, we convert each given measurement:(i) Converting 63 lb to kg: \[ \text{Kilograms} = 63 \times 0.4545 \approx 28.626 \text{ kg} \](ii) Converting 150 lb to kg: \[ \text{Kilograms} = 150 \times 0.4545 \approx 68.175 \text{ kg} \](iii) Converting 2.5 kg to lb: \[ \text{Pounds} = 2.5 \times 2.20 = 5.5 \text{ lb} \](iv) Converting 140 kg to lb: \[ \text{Pounds} = 140 \times 2.20 = 308 \text{ lb} \]

Key Concepts

Kilograms to Pounds Conversion

Converting measurements from kilograms (kg) to pounds (lb) is a crucial skill in international contexts where both units are frequently used. A kilogram is a metric unit of mass, while a pound is commonly used in the United States and some other countries. To convert kilograms to pounds, know that 1 kg is equivalent to approximately 2.20 pounds.
To make the conversion, multiply the weight in kilograms by 2.20. For example, if you have an object weighing 10 kg, its weight in pounds is calculated as:
\[ \text{Pounds} = 10 \times 2.20 = 22 \text{ lb} \]Using the correct conversion factor ensures accurate results, so remember this constant whenever converting between these two units.

Proportional Relationship in Measurements

In measurements, a proportional relationship means that the ratio of one quantity to another remains constant. This principle applies when converting units such as kilograms to pounds. The conversion factor of 2.20 signifies that any weight in kilograms corresponds to 2.20 times that weight in pounds.
Understanding this concept helps ensure consistency and accuracy in conversions. Imagine it as a scaling factor; increase the kilograms, and the pounds increase proportionally at the same rate.
Conversely, to convert pounds to kilograms, use the reciprocal of 2.20, which is approximately 0.4545. This reciprocal indicates how pounds shrink into smaller values in kilograms, facilitating easy transitions back and forth between the two measurements.

Mathematical Equations for Conversion

Mathematical equations make unit conversions more straightforward. For kilograms to pounds, employ the equation:
\[ \text{Pounds} = \text{Kilograms} \times 2.20 \]This equation tells you that multiplying the weight in kilograms by 2.20 will yield the weight in pounds.
Similarly, to convert pounds to kilograms, the equation is:
\[ \text{Kilograms} = \text{Pounds} \times 0.4545 \]Each equation corresponds to the aforementioned conversion factors, helping transition seamlessly between kilograms and pounds. Keeping these equations in your mathematical toolkit provides a reliable method, saving time and reducing errors during calculations.