Problem 34 - Calculate With Confidence

Question

A client’s intake decreased from 2,500 milliliters (mL) per day to 2,000 mL per day. What was the percent of decrease? _____________

Step-by-Step Solution

Answer

20%

Step 1: Understand the Formula

To find the percentage decrease, we use the formula: \[ \text{Percent Decrease} = \left( \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \right) \times 100 \% \]

Step 2: Identify the Original and New Values

In this problem, the original daily intake is 2,500 mL, and the new daily intake is 2,000 mL.

Step 3: Calculate the Change in Value

Subtract the new value from the original value: \( 2,500 \text{ mL} - 2,000 \text{ mL} = 500 \text{ mL} \).

Step 4: Apply the Formula

Substitute the values into the percentage decrease formula: \[\text{Percent Decrease} = \left( \frac{500 \text{ mL}}{2,500 \text{ mL}} \right) \times 100 \%\]

Step 5: Perform the Calculation

First, calculate the fraction: \( \frac{500}{2,500} = 0.2 \). Then multiply by 100 to find the percent decrease: \( 0.2 \times 100 = 20\% \).

Key Concepts

Formula Application for Percentage Decrease

Calculating percentage decrease is essential when understanding how much a quantity has reduced in comparison to its original value. The key formula for percentage decrease is:

• \( \text{Percent Decrease} = \left( \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \right) \times 100 \% \)

This formula serves to express the reduction as a percentage of the original value. It requires two main elements: the original value and the new, reduced value. By comparing how much has been lost relative to the initial amount, we gain a clearer perspective on the extent of the decrease. The process might initially seem daunting, but understanding each part of the formula can help you approach the problem systematically.

Calculating the Change in Value

The process of determining the change in value is a vital step to finding percentage decrease. It can be easily done by subtracting the new value from the original value. Let's illustrate this with our example:

• Original intake: 2,500 mL
• New intake: 2,000 mL

To find the change in value, we perform the subtraction:

• \( 2,500 \text{ mL} - 2,000 \text{ mL} = 500 \text{ mL} \)

This 500 mL represents the decrease in the client's daily intake, which is necessary for the next step in calculating the percentage decrease. Make sure to pay attention to units and ensure consistency in your measurements to avoid errors.

Step-by-Step Solution Simplified

To bring everything from the concept down into practical application, let's break down the percentage decrease calculation into clear, manageable steps using our example:

• Step 1: Recognize the formula: \( \text{Percent Decrease} = \left( \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \right) \times 100 \% \).
• Step 2: Identify values: the original value is 2,500 mL, and the new value is 2,000 mL.
• Step 3: Calculate the change: \( 2,500 \text{ mL} - 2,000 \text{ mL} = 500 \text{ mL} \).
• Step 4: Plug into the formula: \( \text{Percent Decrease} = \left( \frac{500}{2,500} \right) \times 100 \% \).
• Step 5: Perform the math: first divide 500 by 2,500, resulting in 0.2. Then, multiply by 100 to achieve a 20% decrease.

Each of these steps builds upon the previous, simplifying a complex calculation into smaller, more digestible parts. Taking it one step at a time ensures you understand the method and results in an accurate answer.