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Chapter 7: Problem 16

Identify the amount, base, and \(p\) value. \(25 \%\) of 400 cars is 100 cars.

Short Answer

Expert verified
Amount: 100 cars, Base: 400 cars, Percentage (p): 25%

Step by step solution

01

- Identify the percentage (p)

The percentage given in the problem is 25%. Therefore, the value of \(p\) is 25%.
02

- Identify the base

The problem states '25% of 400 cars,' which means the base is 400 cars.
03

- Identify the amount

The problem concludes with 'is 100 cars,' which means the amount is 100 cars.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

percentages
Percentages are a way of expressing a number as a fraction of 100. They are commonly used to represent ratios, proportions, and probability. When you see a percentage, it tells you how many parts of 100 something is. For example, 25% means 25 out of 100.

In our example, we have 25%, which means 25 parts out of every 100 parts.

Understanding percentages is crucial because:
  • They simplify complex ratios.
  • They help in comparing different quantities effectively.
  • They are commonly used in various fields like finance, science, and statistics.
To convert a percentage to a decimal, you divide by 100. So, 25% becomes 0.25. Conversely, to convert a decimal back to a percentage, you multiply by 100.
base value
The base value in a percentage problem is the initial amount or total quantity from which you are calculating the percentage. It serves as the point of reference or the whole from which you will determine the part.

In our example, the base value is 400 cars. This number is essential because:
  • It represents the total quantity we are interested in.
  • It serves as the denominator in the percentage calculation.
  • It helps in understanding the scale of the percentage.
To find the part or amount from the base value using percentage, you multiply the base value by the percentage (in decimal form). For instance, calculating 25% of 400 involves multiplying 400 by 0.25, resulting in 100 cars.
amount calculation
Amount calculation is the process of finding a specific part of the base value using the given percentage. This involves straightforward multiplication.

In our example, the problem asks for 25% of 400 cars, which means we need to find what 25% of 400 is. Here's how to do it step-by-step:
  • Convert the percentage to a decimal: 25% becomes 0.25.
  • Multiply the base value by the decimal: 400 * 0.25 = 100.
  • The result is the amount: 100 cars.
Therefore, 25% of 400 cars is 100 cars. This method can be applied to any percentage problem, making it a versatile tool in math. Always remember:
  • Convert percentages to decimals before multiplying.
  • Double-check your calculations to ensure accuracy.
  • Understand what the amount represents in real-world terms.
This approach makes percentage calculations simple and reliable.

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Most popular questions from this chapter

Solve the problem using a percent equation. \(12 \%\) of what number is \(26.4 ?\)

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Brian has been saving money to buy a 61-in. Samsung Projection HDTV. He has saved \(\$ 1440\) so far, but this is only \(60 \%\) of the total cost of the television. What is the total cost?

Which of the numbers represent \(180 \% ?\) a. 18 b. 1.8 c. \(\frac{9}{5}\) d. \(\frac{9}{5} \%\)
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