Question

A fully fueled AeroTrans 474 passenger jet airplane weighs 987,000 pounds at takeoff. it carries 422,000 pounds of fuel. What percent of the aircraft's takeoff weight is fuel? A. \(23 \%\) B. \(43 \%\) C. \(57 \%\) D. \(77 \%\)

Short answer

B. 43%

Step-by-step solution

- Identify Given Quantities

Identify the weights involved in the problem: the total takeoff weight and the fuel weight. The takeoff weight is 987,000 pounds, and the fuel weight is 422,000 pounds.

- Write the Formula for Percent Calculation

The formula for calculating the percentage is: \[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \]

- Substitute the Given Values into the Formula

Using the given values, the part (fuel weight) is 422,000 pounds and the whole (total takeoff weight) is 987,000 pounds. Substitute these into the formula: \[ \text{Percentage} = \left( \frac{422,000}{987,000} \right) \times 100 \]

- Simplify the Fraction

Simplify the fraction \( \frac{422,000}{987,000} \) to make calculations easier. \[ \frac{422,000}{987,000} \approx 0.4275 \]

- Perform the Multiplication to Find the Percentage

Multiply the simplified fraction by 100 to find the percentage. \[ 0.4275 \times 100 = 42.75 \% \]

- Round to the Nearest Whole Number

Round the result to the nearest whole number, which is 43%.

- Select the Correct Answer

Compare the calculated percentage to the provided answer choices. The correct answer is B. 43%.

Key concepts

math problem solving

Math problem solving involves a series of logical steps to reach a solution. It's essential to break down the problem into manageable parts. In this exercise, the first step is understanding the given values: the airplane's takeoff weight and the fuel weight. Solving a math problem often requires finding a relevant formula and then carefully substituting the provided values into that formula. This structured approach helps simplify complex problems and makes it easier to find the correct solution. Remember that verifying and comparing your final answer with the given options ensures accuracy.

percentages

Percentages represent a fraction of 100. In this problem, the aim is to find what percent of the airplane's total weight is made up of fuel. The formula for calculating a percentage is \( \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \). Here, 'Part' is the weight of the fuel (422,000 pounds), and 'Whole' is the total takeoff weight (987,000 pounds). By substituting these values into the formula and multiplying by 100, you convert the decimal outcome into a percentage. Understanding percentages is crucial in many areas such as finance, statistics, and daily life scenarios.

ratio and proportion

Ratio and proportion are fundamental concepts in mathematics that are closely related to percentages. They help to compare quantities. A ratio represents a relationship between two numbers, showing how many times one value contains or is contained within the other. In this example, the ratio of the fuel weight to the total takeoff weight is \( \frac{422,000}{987,000} \), which simplifies to 0.4275. This ratio is then converted into a proportion when you multiply by 100 to find the percentage. Ratios and proportions allow us to make sense of fractions and can be applied in various mathematical contexts, including scale models and recipes.

step-by-step solution

A step-by-step solution ensures clarity and helps you methodically work through a problem. Let's break down the exercise: First, identify the necessary values (takeoff and fuel weights). Next, use the percentage formula to relate these values. Insert the numbers into the formula, simplify if possible, and then perform the arithmetic operations. Rounding the final answer to the nearest whole number is usually the last step, and selecting the correct multiple-choice answer concludes the solution. This methodical approach not only helps in solving the problem but also in understanding the reasoning behind each calculation.