Problem 24 - Prealgebra

Question

Carbon constitutes \(18.5 \%\) of the human body by weight. Determine the amount of carbon contained in a person who weighs 145 pounds. Round to the nearest tenth.

Step-by-Step Solution

Answer

A person weighing 145 pounds contains 26.8 pounds of carbon.

Step 1: Understand the Problem

We are given that carbon makes up 18.5% of the human body by weight, and we need to find out how much carbon is present in a person who weighs 145 pounds.

Step 2: Formula for Calculating Carbon Weight

To find the weight of carbon in the body, we can use the formula: \[\text{Weight of Carbon} = \frac{\text{Percentage of Carbon}}{100} \times \text{Total Weight of Person}\]

Step 3: Substitute Known Values

Substitute the given values into the formula:\[\text{Weight of Carbon} = \frac{18.5}{100} \times 145\]

Step 4: Perform the Calculation

Calculate the value:\[\text{Weight of Carbon} = 0.185 \times 145 = 26.825\]This results in approximately 26.825 pounds of carbon.

Step 5: Round to the Nearest Tenth

Round 26.825 to the nearest tenth, which gives us 26.8.

Key Concepts

Understanding Carbon Content in Human Body

Carbon is one of the most fundamental elements for life. It plays a crucial role in various biological processes. In fact, carbon accounts for a significant percentage of a person’s body weight. For most humans, approximately 18.5% of their total body weight is composed of carbon.
This percentage implies that if you know the body weight of an individual, you can determine how much of that weight is carbon. Understanding the proportional weight of carbon in the body helps provide insight into how matter and essential elements are distributed in living organisms.

The Basics of Weight Calculation Using Percentages

Calculating weight using percentages is a straightforward process. You can determine the weight of any constituent part of a larger whole by using simple multiplication. Here's how it works:

• Identify the total weight or value you are working with. In our exercise, it's the weight of 145 pounds.
• Find the percentage that the constituent represents in the total. For instance, 18.5% for carbon content.
• Convert the percentage into its decimal form. This is done by dividing the percentage by 100. Thus, 18.5% becomes 0.185.
• Multiply the total weight by this decimal to find the weight of the particular component. So, here it’s 145 pounds multiplied by 0.185.

Using these steps allows straightforward calculation of how much of a particular element, such as carbon, contributes to the total weight.

Rounding Numbers to the Nearest Tenth

When dealing with weight calculations or any numerical data, precision is key. Rounding helps simplify numbers to make them easier to understand and communicate. To round to the nearest tenth, follow these steps:

• Look at the number in the hundredths place (the second place after the decimal point).
• If this digit is 5 or higher, increase the digit in the tenths place by one. If it's 4 or lower, keep the tenths place digit the same.
• Remove all digits beyond the tenths place after rounding.

In our calculation, we found the carbon weight to be 26.825 pounds. The digit in the hundredths place is a 2, so we round down. The rounded number becomes 26.8. This process ensures the final number remains concise and as accurate as needed for practical purposes.