Problem 33 - Calculate With Confidence

Question

A client’s weight increased from 120 lb to 132 lb. What was the percent of increase in body weight? _______________

Step-by-Step Solution

Answer

The percent increase in body weight is 10%.

Step 1: Understand the Problem

To find the percent increase in body weight, we need to compare the original weight with the new weight and calculate the increase percentage.

Step 2: Calculate the Increase in Weight

Subtract the original weight from the new weight to find the increase: \[\text{Increase} = 132 \text{ lb} - 120 \text{ lb} = 12 \text{ lb}\]

Step 3: Use the Percent Increase Formula

Use the formula for percent increase: \[\text{Percent Increase} = \left(\frac{\text{Increase}}{\text{Original Value}}\right) \times 100\]Substitute the known values:\[\text{Percent Increase} = \left(\frac{12}{120}\right) \times 100 = 10\%\]

Key Concepts

Understanding the Percent Increase Formula

To solve problems involving percentage changes, the percent increase formula is essential. This formula helps determine how much a quantity has increased relative to its original value. The formula is written as:\[\text{Percent Increase} = \left(\frac{\text{Increase}}{\text{Original Value}}\right) \times 100\]Here’s how it works:

• Increase: It is calculated by subtracting the original value from the new value.
• Original Value: The starting point or initial amount before the change occurs.
• Compute: Divide the increase by the original value to find the relative increase, and then multiply by 100 to get a percentage.

Understanding this formula is crucial for any problem involving percentage growth. Whether it’s calculating weight change or financial growth, the same rule applies. Using this, you can easily gauge any increase as a proportion of its original amount.

Calculating Weight Increase

In many real-world scenarios, assessing weight change is important. To find out how much someone’s weight has increased, we start by identifying the original and new weights. For example, if a person's weight rises from 120 lb to 132 lb, the process is straightforward:First, calculate the absolute increase in weight:\[\text{Weight Increase} = \text{New Weight} - \text{Original Weight} = 132 \text{ lb} - 120 \text{ lb} = 12 \text{ lb}\]
This simple subtraction tells you the exact pounds added. For real-world applications like managing a fitness plan or assessing health risks, this calculation is essential. It gives you a clear picture of changes over time.

Problem Solving with Mathematics

Solving mathematical problems, like finding the percent increase, involves several steps. It is important to approach each problem methodically. Here’s a quick guide:

• Understand the Problem: Clearly define what you're being asked to find.
• Identify Known Variables: Determine the original value and new value. They act as the foundation for calculations.
• Apply Mathematical Formulas: Use the appropriate formulas, like the percent increase formula, to reach the solution.
• Verify the Solution: Always check your calculations to avoid errors.

This structured approach not only provides correct answers but also enhances your mathematical reasoning. It builds confidence in tackling a wide range of problems, whether academic or practical.

Basics of Arithmetic

Arithmetic is the foundation of math, used daily in practical scenarios. It includes basic operations like addition, subtraction, multiplication, and division. For our weight problem, the key operation was subtraction to find the increased weight:First:\[132 \text{ lb} - 120 \text{ lb} = 12 \text{ lb}\]
Next, we applied division when using the percent increase formula:\[\frac{12}{120} = 0.1\]
Followed by multiplication:\[0.1 \times 100 = 10\%\]
These simple but powerful operations are building blocks for solving everyday math problems. Mastery of basic arithmetic fosters a strong foundation for more complex mathematics, making problem-solving a smoother and more intuitive process.