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Chapter 2: Problem 120

(a) \(150 \%\) of 90 is what number? (b) \(6.4 \%\) of what amount is \(\$ 2.88 ?\) (a) 50 is what percent of \(40 ?\)

Short Answer

Expert verified
(a) 135 (b) 45 (c) 125%

Step by step solution

01

Understanding Percentages

To find a percentage of a number, convert the percentage to a decimal by dividing by 100, then multiply by the number.
02

Calculate 150% of 90

Convert 150% to a decimal: \(150\text{\%} = 1.50\). Now multiply by 90: \(1.50 \times 90 = 135\)
03

Setup the Equation for part (b)

Use the formula: \( \text{Percentage} \times \text{Total Amount} = \text{Given Amount} \). Set up the equation as follows: \(0.064 \times T = 2.88\), where \( T \) is the total amount.
04

Solve for the Total Amount

To find \( T \), divide both sides by 0.064: \( T = \frac{2.88}{0.064} = 45\)
05

Understanding part (c)

To find what percent one number is of another, set up a ratio and convert to a percentage by multiplying by 100.
06

Calculate the Percentage for part (c)

Set up the ratio as \( \frac{50}{40} \). Simplify the ratio: \( \frac{50}{40} = 1.25\). Convert to a percentage: \( 1.25 \times 100\text{\%} = 125\text{\%}\)

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Key Concepts

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

percent of a number
A fundamental concept in percentage calculations is finding what percent a specific number (part) is of another number (whole). We often use this to compare values.
To calculate the percent of a number:
  • Convert the percentage to a decimal by dividing the percentage by 100.
  • Multiply this decimal by the given number.
For example, to find out what 150% of 90 is, convert 150% to decimal (150% 梅 100 = 1.50), then multiply by 90: \[1.50 \times 90 = 135\].
An important point to remember is that percentages over 100% simply mean more than the whole (like 150% of 90 being greater than 90).
converting percentages to decimals
Converting percentages to decimals is a crucial step in many percentage calculations.
It simplifies multiplication and division. To convert:
  • Simply divide the percentage by 100.
For example, converting 64% to decimal: \[64\text{\textpercent} \rightarrow \frac{64}{100} = 0.64\]
This conversion is handy when solving word problems, such as finding what amount 6.4% of another amount equals. Here, convert 6.4% to decimal: \[6.4\text{\textpercent} = 0.064\]. Then use it in the formula:
  • \text{Percentage} \times \text{Total Amount} = \text{Given Amount}
So, you can set up the equation: \[0.064 \times T = 2.88\], solve for T, giving \[T = \frac{2.88}{0.064} = 45\]. This method ensures a clear and accurate calculation.
ratio and proportion
Ratios and proportions are often used in percentage calculations to understand the relation between two numbers.
A ratio is a comparison of two numbers, showing how many times one value contains another. To find what percent 50 is of 40:
  • Set up a ratio: \[\frac{50}{40}\].
  • Simplify the ratio: \[\frac{50}{40} = 1.25\].
  • Convert to a percentage by multiplying by 100: \[1.25 \times 100 = 125\text{\textpercent}\].
This tells us that 50 is 125% of 40. Understanding this process helps solve many real-life problems where comparisons are necessary.

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Most popular questions from this chapter

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. \(2(3 x-1)<4\) or \(3 x-5>1\)

Solve. Noe installs and configures software on home computers. He charges \(\$ 125\) per job. His monthly expenses are \(\$ 1,600\). How many jobs must he work in order to make a profit of at least \(\$ 2,400 ?\)

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