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Chapter 7: Problem 15

Identify the amount, base, and \(p\) value. 12 balloons is \(60 \%\) of 20 balloons.

Short Answer

Expert verified
Amount: 12 balloons, Base: 20 balloons, Percentage: 60%.

Step by step solution

01

Identify the base value

The base value is the total number of balloons. In the statement, 20 balloons is the base value.
02

Identify the amount

The amount is the number of balloons that correspond to the given percentage. In the statement, 12 balloons represent the amount.
03

Identify the percentage (\boldsymbol{p}) value

The percentage is the part of the base that the amount represents. In the statement, 12 balloons is 60% of 20 balloons, meaning the percentage is 60%.

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Key Concepts

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

base value
The base value in a percentage calculation is the total or whole amount to which a percentage is being compared. In our exercise, the base value is 20 balloons. This is because the percentage calculation (60% of 20 balloons) uses 20 as the reference.
To identify the base value, look for the total quantity you are discussing or analyzing. For example:
  • In a class of 30 students, if 15 passed an exam, the base value is 30.
  • If a store had 100 items and sold 40, the base value is 100.
Understanding the base value is crucial, as it sets the context for the percentage and the amount.
Remember, the base value is always the starting point in percentage problems. It is what the percentage and the amount will be calculated from.
amount
The amount in a percentage calculation is the part, share, or portion of the base value that is represented by the percentage. In our example, the amount is 12 balloons. This is because 12 balloons are 60% of the 20 balloons (the base value).

To determine the amount in percentage problems, follow these straightforward steps:
  • Start by identifying the base value and the percentage.
  • Calculate the part of the base represented by the percentage using the formula:
    \texample \text: if you want to calculate 60% of 20, you multiply:
\[Amount = \frac{Percentage}{100} \times Base\]
  • For example:\[Amount = \frac{60}{100} \times 20 = 12\]
    • Recognizing the amount helps you understand how much of the total you are dealing with and can be crucial in various real-life contexts, such as finance, statistics, and science.
    percentage
    A percentage is a way of expressing a number as a part of a whole. It is a fraction of 100. In our example, 60% means that 12 balloons are 60% of the 20 balloons (the base value).
    Here is how to find the percentage correctly:
    • The formula for percentage calculation is:
      \[Percentage = \frac{Amount}{Base} \times 100\]
    • Example: If we take our example with 12 balloons and 20 total balloons:
      \[Percentage = \frac{12}{20} \times 100 = 60\text{ percent}\]
    Using percentages helps to simplify comparisons and understand proportions in various scenarios, from school grades to financial discounts and statistics. By mastering percentage calculations, you'll find it easier to navigate through numbers and data efficiently.

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    Most popular questions from this chapter

    Solve the problem using a percent equation. What is \(32 \%\) of \(30 ?\)

    Which of the numbers represent \(125 \% ?\) a. 1.25 b. 0.125 c. \(\frac{5}{4}\) d. \(\frac{5}{4} \%\)

    During a weak economy, milk prices increased during a 1 -year period. The average price in 2008 was \(\$ 3.90 .\) If this value is \(126 \%\) of the price from 2007 , determine the price in 2007 . Round to two decimal places. (Source: U.S. Department of Agriculture)

    Mr. Asher made \(\$ 49,000\) as a teacher in Virginia in \(2007,\) and he spent \(\$ 8,800\) on food that year. In \(2008,\) he received a \(4 \%\) increase in his salary, but his food costs increased by \(6.2 \%\) a. How much money was left from Mr. Asher's 2007 salary after subtracting the cost of food? b. How much money was left from his 2008 salary after subtracting the cost of food? Round to the nearest dollar.

    Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{1}{13}$$
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