Problem 19 - Prealgebra

Question

Solve each of these problems using the method developed in this section. According to the Centers for Disease Control and Prevention (CDC), more than \(60 \%\) of U.S. adults are overweight, and about \(15 \%\) of children and adolescents ages 6 to 19 are overweight. Your friend decides to go on a diet and goes from 155 pounds to 130 pounds over a 4 month period. What was her percentage weight loss? Round your answer to the nearest percent.

Step-by-Step Solution

Answer

Her percentage weight loss is approximately 16%.

Step 1: Understand the Problem

The problem asks us to find the percentage weight loss of your friend, who initially weighed 155 pounds and now weighs 130 pounds.

Step 2: Calculate the Weight Loss

Subtract the final weight from the initial weight to find the amount of weight lost. Weight loss = Initial weight - Final weight = 155 lbs - 130 lbs = 25 lbs.

Step 3: Calculate the Percentage Weight Loss

To find the percentage weight loss, divide the weight loss by the initial weight and multiply by 100 to convert it to a percentage. Percentage weight loss = \( \frac{25}{155} \times 100 \approx 16.13 \% \).

Step 4: Round the Percentage

Since we need to round our answer to the nearest percent, we round 16.13% to 16%.

Key Concepts

Weight Loss Percentage

Understanding how to calculate weight loss percentage is key for anyone looking to track their progress accurately. To determine weight loss percentage, you compare the amount of weight lost to the original weight. This gives you a mathematical representation of how much of the initial body weight has been shed.

Here's how the calculation works:

• Start by identifying the initial weight. For instance, in our scenario, it was 155 pounds.
• Next, find out the final weight after the weight loss journey, which was 130 pounds here.
• Subtract the final weight from the initial weight to get the total weight lost. In this example, that results in 25 pounds.
• Finally, use the formula for percentage weight loss: \[\text{Percentage Weight Loss} = \left(\frac{\text{Weight Loss}}{\text{Initial Weight}}\right) \times 100\] Plugging in the values gives: \[ \frac{25}{155} \times 100 \approx 16.13\% \]

The calculation tells us that our friend's weight loss is approximately 16%.

Problem-Solving Steps

Breaking down complex weight loss calculations into simpler, more manageable steps is crucial for success. It helps keep problems from becoming overwhelming, and keeps you on track.

• Understand the Problem: Clearly define what is being asked. In our problem, this involved grasping the initial and final weights.
• Calculate the Weight Loss: The difference between the initial weight and final weight will give the total pounds lost.
• Calculate the Percentage: Finally, convert this loss into a percentage of the initial weight to better understand the change.
• Round Off: Since precision is not overly critical here, rounding to the nearest whole percentage can simplify the result.

Rounding was necessary because 16.13% can be more reasonably expressed as 16%, a clearer and more concise whole number.

Basic Arithmetic Operations

Basic arithmetic operations lie at the heart of all percentage calculations, including those for weight loss. These operations involve addition, subtraction, multiplication, and division.

• Subtraction: This is used to determine how much weight has been lost, by subtracting the final weight from the initial weight.
• Division and Multiplication: To convert the weight loss into a percentage, you divide the weight loss by the initial weight, which gives you a decimal. Multiplying this by 100 converts the decimal into a percentage.

Each of these steps requires a solid grasp of basic arithmetic, as each operation builds on the previous to reach the final answer.

Arithmetic isn't just about numbers; it's about understanding relationships and finding ways to express those relationships clearly. Whether you're calculating the change in a person’s weight or applying similar principles to other areas, the foundation is always the same.