Question

Susan unloaded 168 boxes of books from a shipment of 1052. What percentage of the shipment is left to unload? (Round to a whole number.) A. \(16 \%\) B. \(48 \%\) C. \(84 \%\) D. \(86 \%\)

Short answer

The percentage of the shipment left to unload is 84% (Option C).

Step-by-step solution

- Determine the Percentage of Boxes Unloaded

Calculate the percentage of boxes Susan unloaded by using the formula: \[ \text{Percentage Unloaded} = \left( \frac{\text{Number of Boxes Unloaded}}{\text{Total Number of Boxes}} \right) \times 100 \] Plugging in the numbers: \[ \text{Percentage Unloaded} = \left( \frac{168}{1052} \right) \times 100 \] Use a calculator to find the result.

- Calculate the Percentage Unloaded

Now, divide 168 by 1052 and then multiply by 100 to find the percentage: \[ \frac{168}{1052} \approx 0.1597 \] Then multiply by 100: \[ 0.1597 \times 100 = 15.97 \] Rounding this to the nearest whole number gives 16d.

- Calculate the Percentage of Boxes Left to Unload

Subtract the percentage of boxes unloaded from 100% to find the percentage of boxes left to unload: \[ \text{Percentage Left to Unload} = 100\% - 16\% = 84\% \]

- Choose the Correct Answer

Based on the calculation, the percentage of the shipment left to unload is 84%. Thus, the correct answer is option C.

Key concepts

percentage formula

Calculating percentages is a vital skill in both mathematics and real-world applications. To calculate the percentage, you use the formula: \[ \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \] Here, the 'part' represents the number you are interested in (e.g., boxes unloaded), and the 'whole' is the total quantity (e.g., total boxes). This formula helps you determine what fraction or portion (the part) the whole stands for, converted into a percentage. This formula is universal and can be used in many different scenarios, from calculating discounts in shopping to analyzing data in scientific research.

word problems

Word problems often appear complex, but breaking them into smaller manageable parts makes them easier to solve. Start by identifying the important numbers and the question being asked. For instance, in our exercise: \[ \text{Susan unloaded 168 boxes out of 1052, and we need to find the percentage left to unload.} \] Once you identify these numbers, you can apply the relevant mathematical formulas and operations. Word problems also improve critical thinking and problem-solving skills, as they require you to apply math in practical and often everyday situations.

basic arithmetic operations

Having a strong understanding of basic arithmetic operations (addition, subtraction, multiplication, and division) serves as the foundation for solving percentage problems. Let's break down the arithmetic steps in our problem: \[ - Division: Divide the number of boxes unloaded by the total number of boxes: \frac{168}{1052} \] \[ - Multiplication: Multiply the result by 100 to convert it into a percentage: 0.1597 \times 100 \] \[ - Rounding: Round the result to the nearest whole number to get 16%. \] \[ - Subtraction: Subtract the unloaded percentage from 100% to find what's left: 100\text{%} - 16\text{%} = 84\text{%} \] Practicing these basic operations will improve your ability to solve more complex problems efficiently. Remember, arithmetic is the backbone of all math-related exercises.