Problem 27 - Algebra 1

Question

Solve the percent problem. 62 hours is what percent of 3 days?

Step-by-Step Solution

Answer

The 62 hours is approximately 86.11% of 3 days.

Step 1: Convert Days into Hours

Since 1 day is equivalent to 24 hours, 3 days will be equivalent to \(3 * 24 = 72\) hours.

Step 2: Apply the Percentage Formula

The formula to calculate percentage is \((\frac{part}{whole})*100\). Replace 'part' with 62 (the given hours) and 'whole' with 72 (the total hours in 3 days). Therefore, calculate \((\frac{62}{72})*100\).

Step 3: Calculate the Percentage

Proceed with the calculation to find the percentage value.

Key Concepts

Understanding Percentage Calculation

Percentage calculations allow us to express a number as a fraction of 100, making it easier to compare proportions. To solve any percent problem, we generally use the formula:

• \( \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \)

In this scenario, 62 hours is the 'part' and 72 hours is the 'whole'. By inserting these values into the formula, we calculate the percentage of hours worked compared to the total available hours in three days:

• \( \text{Percentage} = \left( \frac{62}{72} \right) \times 100 = 86.11\% \)

The result, 86.11%, shows how 62 hours constitute 86.11% of 3 days in terms of hours.

Conversion of Units Made Simple

Before diving into percentage calculations, it's essential to ensure all quantities share the same unit. This exercise requires converting days to hours. Knowing that 1 day equals 24 hours simplifies this process. We calculate the conversion by multiplying the number of days by the number of hours in a day:

• \( 3 \times 24 = 72 \text{ hours} \)

Now, both quantities - the given 62 hours and the 72 hours (3 days) - are in the same unit, making it possible to proceed with the percentage calculation.

Applying Mathematical Reasoning

Mathematical reasoning involves logical thinking to solve problems step-by-step. Here, we begin by addressing the conversion and then apply the percentage formula. This logical sequence ensures accuracy and understanding.

• Identify: Recognize the problem requires converting days into hours so both quantities are comparable.
• Convert: Change 3 days into 72 hours. This aligns units.
• Calculate: Use the percentage formula to find what percent the 62 hours is of 72 hours.

By following this structured approach, we ensure that every part of the problem is understood and addressed thoroughly, leading to the correct solution.