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Chapter 7: Problem 20

Identify the amount, base, and \(p\) value. \(175 \%\) of 2 in. of rainfall is 3.5 in.

Short Answer

Expert verified
Amount: 3.5 in., Base: 2 in., \(p\) value: 175%

Step by step solution

01

Identify the given percentage (p)

The given percentage in the problem is 175%. This is your value for \(p\).
02

Identify the base amount

The base amount is the original quantity before any percentage is applied. In this case, it is 2 in. of rainfall.
03

Identify the resulting amount

The resulting amount after applying the percentage to the base is 3.5 in. of rainfall.
04

Verify the relationship

Check if 175% of 2 in. equals 3.5 in. by calculating \( \frac{175}{100} \times 2 = 3.5 \). The relationship holds true.

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Key Concepts

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

percentage calculation
Percentage calculation often confuses students, but it is quite simple once you understand the basics. A percentage is a way to express a number as a fraction of 100. For instance, 175% means 175 out of 100.
To calculate a percentage of a number, you can use the formula:
\(\text{Percentage of base} = \frac{p}{100} \times \text{base} \).
Here鈥檚 how you apply it:
  • Identify the percentage value, for example, 175%.
  • Convert the percentage to a decimal by dividing it by 100 (175 梅 100 = 1.75).
  • Multiply this decimal by the base amount (1.75 脳 2 in = 3.5 in).
By following these steps, you will be able to find the resulting amount easily.
base amount
The base amount is the initial value or the original quantity before any percentage is applied. Understanding this helps you recognize what percentage affects.
In the given problem, the base amount is 2 inches of rainfall.
  • It is the reference point from which you compute the percentage.
  • Here, the 2 inches is the base, and various percentages (like 175%) modify this base.
The base is crucial because it sets the foundation for all further calculations.
resulting amount
The resulting amount is what you get after applying the percentage to the base amount. In short, it鈥檚 the new value obtained.
For example, when you have 175% of 2 inches of rainfall, the resulting amount is 3.5 inches.
  • First, identify the base amount (2 inches).
  • Next, apply the percentage (175%) to this base by converting the percentage into a decimal (175% 梅 100 = 1.75).
  • Then, multiply the decimal by the base (1.75 脳 2 in = 3.5 in).
This process makes it clear that the resulting amount of rainfall is 3.5 inches after applying 175% to the base of 2 inches.

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