<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation

3.10: Percent Equations

Difficulty Level: At Grade Created by: CK-12
Atoms Practice
Estimated9 minsto complete
%
Progress
Practice Percent Equations
 
 
 
MEMORY METER
This indicates how strong in your memory this concept is
Practice
Progress
Estimated9 minsto complete
%
Estimated9 minsto complete
%
Practice Now
MEMORY METER
This indicates how strong in your memory this concept is
Turn In

Suppose that there was an article in your school newspaper that said that 80% of the students in your school plan on attending the prom. It also said that 500 students in your school plan on attending the prom. Would you be able to tell from this information how many students there are in your school? In this Concept, you'll learn how to solve equations involving percentages so that you can determine information such as this.

Watch This

For more help with percent equations, watch this 4-minute video recorded by Ken’s MathWorld. How to Solve Percent Equations (4:10)

Guidance

Now that you remember how to convert between decimals and percents, you are ready for the percent equation:

\begin{align*}part = \% \ rate \times base\end{align*}

The key words in a percent equation will help you translate it into a correct algebraic equation. Remember the equal sign symbolizes the word “is” and the multiplication symbol symbolizes the word “of.”

Example A

Find 30% of 85.

Solution: You are asked to find the part of 85 that is 30%. First, translate into an equation:

\begin{align*}n=30\% \times 85\end{align*}

Convert the percent to a decimal and simplify:

\begin{align*}n & =0.30 \times 85 \\ n & =25.5\end{align*}

Example B

A dime is worth what percent of a dollar?

Solution:

Since a dime is 10 cents and a dollar is 100 cents, we can set up the following equation:

\begin{align*}\frac{10}{100}=10%\end{align*}

Example C

50 is 15% of what number?

Solution: Translate into an equation:

\begin{align*}50 = 15\% \times w\end{align*}

Rewrite the percent as a decimal and solve:

\begin{align*}50 & = 0.15 \times w \\ \frac{50}{0.15} & = \frac{0.15 \times w}{0.15} \\ 333 \frac{1}{3} & = w\end{align*}

Guided Practice

6 is 2% of what number?

Solution:

First, use the percent equation:

\begin{align*}6=2% \times n\end{align*}

We can also use the fractional form of a percentage. Substitute in \begin{align*}\frac{2}{100}\end{align*} for 2%, since they are equivalent expressions:

\begin{align*} & 6= \frac{2}{100} \times n\\ &\frac{100}{2}\times 6=\frac{100}{2} \times \frac{2}{100} \times n\\ &\frac{600}{2}= n\\ & 300 = n\\ \end{align*}

6 is 2% of 300.

Practice

Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK-12 Basic Algebra: Percent Problems (14:15)

Answer the following.

  1. 32% of 600 is what number?
  2. 50% of $9.00 is what number?
  3. \begin{align*}\frac{3}{4}\%\end{align*} of 16 is what number?
  4. 9.2% of 500 is what number
  5. 8 is 20% of what number?
  6. 99 is 180% of what number?
  7. What percent of 7.2 is 45?
  8. What percent of 150 is 5?
  9. What percent of 50 is 2500?
  10. $3.50 is 25% of what number?

Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Show More

Vocabulary

Percent Equation

The percent equation can be stated as: "Rate times Total equals Part," or "R% of Total is Part."

Image Attributions

Show Hide Details
Description
Difficulty Level:
At Grade
Grades:
8 , 9
Date Created:
Feb 24, 2012
Last Modified:
Aug 31, 2016
Files can only be attached to the latest version of Modality
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 
MAT.ARI.760.L.1
Here