CHAPTER 4 Ratio, Proportion, and Percent
4.4 Solve General Applications of Percent
Learning Objectives
By the end of this section, you will be able to:
- Translate and solve basic percent equations
- Solve applications of percent
- Find percent increase and percent decrease
Translate and Solve Basic Percent Equations
In the last section, we solved percent problems by setting them up as proportions. That is the best method available when you did not have the tools of algebra. Now, in this section we will translate word sentences into algebraic equations, and then solve the percent equations.
We’ll look at a common application of percent—tips to a server at a restaurant—to see how to set up a basic percent application.
When Kim and her friends went on a road trip to Vancouver, they ate lunch at Marta’s Cafe Tower. The bill came to . They wanted to leave a tip. What amount would the tip be?
To solve this, we want to find what amount is of . The is called the base. The amount of the tip would be , or See (Figure 1). To find the amount of the tip, we multiplied the percent by the base.
A tip for an restaurant bill comes out to .
In the next examples, we will find the amount. We must be sure to change the given percent to a decimal when we translate the words into an equation.
EXAMPLE 1
What number is of
| Translate into algebra. Let the number. | |
| Multiply. | |
| is of |
TRY IT 1.1
What number is of
Show answer
36
TRY IT 1.2
What number is of
Show answer
33
EXAMPLE 2
of is what number?
| Translate into algebra. Let the number. | |
| Multiply. | |
| of is . |
Remember that a percent over is a number greater than . We found that of is , which is greater than .
TRY IT 2.1
of is what number?
Show answer
117
TRY IT 2.2
of is what number?
Show answer
126
In the next examples, we are asked to find the base.
EXAMPLE 3
Translate and solve: is of what number?
| Translate. Let the number. | |
| Divide both sides by 0.75. | |
| Simplify. |
TRY IT 3.1
is of what number?
Show answer
68
TRY IT 3.2
is of what number?
Show answer
64
EXAMPLE 4
of what number is
| Translate. Let the number. | |
| Divide both sides by 0.065. | |
| Simplify. |
TRY IT 4.1
of what number is
Show answer
$26
TRY IT 4.1
of what number is
Show answer
$36
In the next examples, we will solve for the percent.
EXAMPLE 5
What percent of is
| Translate into algebra. Let the percent. | |
| Divide by 36. | |
| Simplify. | |
| Convert to decimal form. | |
| Convert to percent. |
TRY IT 5.1
What percent of is
Show answer
75%
TRY IT 5.2
What percent of is
Show answer
80%
EXAMPLE 6
is what percent of
| Translate into algebra. Let the percent. | |
| Divide by 96. | |
| Simplify. | |
| Convert to percent. |
TRY IT 6.1
is what percent of
Show answer
125%
TRY IT 6.2
is what percent of
Show answer
175%
Solve Applications of Percent
Many applications of percent occur in our daily lives, such as tips, sales tax, discount, and interest. To solve these applications we’ll translate to a basic percent equation, ju