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Chapter 7: Problem 50

Solve the problem using a percent equation. What percent of 25 is \(18 ?\)

Short Answer

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Step by step solution

01

Understand the percent equation

The percent equation is given by \[ \text{percent} \times \text{whole} = \text{part} \]. Here, 'whole' is 25, 'part' is 18, and we need to find the 'percent'.
02

Set up the equation

Rewrite the percent equation with the given values: \[ p \times 25 = 18 \]. Here, 'p' represents the percent expressed as a decimal.
03

Solve for the percent 'p'

Divide both sides of the equation by 25 to isolate p: \[ p = \frac{18}{25} \].
04

Convert the decimal to a percentage

Convert the decimal to a percentage by multiplying by 100: \[ p \times 100 = \frac{18}{25} \times 100 \] which simplifies to 72%. Therefore, 72% of 25 is 18.

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Key Concepts

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

Percent Problem
Understanding percent problems is crucial in our everyday lives. They involve finding what percentage one number is of another. In this exercise, the question is, 'What percent of 25 is 18?' You know the part (18) and the whole (25), but you need to find the percentage. The formula to use here is: \[ \text{percent} \times \text{whole} = \text{part} \]. This relationship helps you set up the problem correctly to find the percent.
Basic Algebra
Basic algebraic skills are needed to solve percent problems. In this case, you need to solve for the unknown percent, represented as 'p.' Once you have the percent equation \[ p \times 25 = 18 \], you only need simple steps to isolate 'p'. Divide both sides of the equation by the whole number (25): \[ p = \frac{18}{25} \]. This step is straightforward but fundamental in solving the problem.
Fraction to Decimal Conversion
After isolating 'p', you get \[ p = \frac{18}{25} \]. This fraction needs to be converted to a decimal to find the percentage. Dividing the numerator by the denominator helps: \[ \frac{18}{25} = 0.72 \]. Understanding how to convert fractions to decimals is crucial, as decimals are often more easily interpreted when working with percentages.
Percentage Calculation
Once you have the decimal form of the percent, converting it to a percentage is simple. Multiply the decimal by 100: \[ 0.72 \times 100 = 72\text{ percent} \]. So, 72% of 25 is 18. This step completes the problem and shows how understanding the entire process from setting up the equation, solving through basic algebra and converting fractions to decimals ultimately leads to calculating the exact percentage. Regular practice with these steps strengthens your skills in percentage calculations and helps in various real-life applications.

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Most popular questions from this chapter

The amount of 8000 dollar is invested at \(4 \%\) for 3 years. a. Compute the ending balance if the bank calculates simple interese? b. Compute the ending balance if the bank calculates interest compounded annually. c. How much more interest is earned in the account with compound interest? (TABLE CAN NOT COPY)

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{1}{15}$$

Convert the decimal to a percent. $$1.014$$

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{6}{7}$$

Convert the fraction to a percent. $$\frac{14}{9}$$
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