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Study Guides > Prealgebra

Solving Applications With Percent

Learning Outcomes

  • Calculate the tip for a meal given a percent
  • Find total recommended amount of fiber and sodium given percent and amount
  • Calculate percent calories from fat given total calories and calories from fat
 

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, just like those we solved in the previous examples in this section. Once you translate the sentence into a percent equation, you know how to solve it. We will update the strategy we used in our earlier applications to include equations now. Notice that we will translate a sentence into an equation.

Solve an application

  1. Identify what you are asked to find and choose a variable to represent it.
  2. Write a sentence that gives the information to find it.
  3. Translate the sentence into an equation.
  4. Solve the equation using good algebra techniques.
  5. Check the answer in the problem and make sure it makes sense.
  6. Write a complete sentence that answers the question.
  Now that we have the strategy to refer to, and have practiced solving basic percent equations, we are ready to solve percent applications. Be sure to ask yourself if your final answer makes sense—since many of the applications we'll solve involve everyday situations, you can rely on your own experience.  

example

Dezohn and his girlfriend enjoyed a dinner at a restaurant, and the bill was [latex]\text{\$68.50}[/latex]. They want to leave an [latex]\text{18%}[/latex] tip. If the tip will be [latex]\text{18%}[/latex] of the total bill, how much should the tip be? Solution
What are you asked to find? the amount of the tip
Choose a variable to represent it. Let [latex]t=[/latex] amount of tip.
Write a sentence that give the information to find it. The tip is 18% of the total bill.
Translate the sentence into an equation. .
Multiply. [latex]t=12.33[/latex]
Check. Is this answer reasonable?
If we approximate the bill to [latex]\text{\$70}[/latex] and the percent to [latex]20\text{%}[/latex], we would have a tip of [latex]\text{\$14}[/latex]. So a tip of [latex]\text{\$12.33}[/latex] seems reasonable.
Write a complete sentence that answers the question. The couple should leave a tip of [latex]\text{\$12.33}[/latex].
 

try it

[ohm_question]146694[/ohm_question]
In the next video we show another example of finding how much tip to give based on percent. https://youtu.be/yFaa2CMx9rk

example

The label on Masao's breakfast cereal said that one serving of cereal provides [latex]85[/latex] milligrams (mg) of potassium, which is [latex]\text{2%}[/latex] of the recommended daily amount. What is the total recommended daily amount of potassium? The figures shows the nutrition facts for cereal.

Answer: Solution

What are you asked to find? the total amount of potassium recommended
Choose a variable to represent it. Let [latex]a=[/latex] total amount of potassium.
Write a sentence that gives the information to find it. [latex]85[/latex] mg is [latex]2\text{%}[/latex] of the total amount.
Translate the sentence into an equation. .
Divide both sides by [latex]0.02[/latex]. .
Simplify. [latex]4,250=a[/latex]
Check: Is this answer reasonable?
Yes. [latex]2\text{%}[/latex] is a small percent and [latex]85[/latex] is a small part of [latex]4,250[/latex].
Write a complete sentence that answers the question. The amount of potassium that is recommended is [latex]4250[/latex] mg.

 

try it

[ohm_question]146697[/ohm_question] [ohm_question]146702[/ohm_question]
 

example

Mitzi received some gourmet brownies as a gift. The wrapper said each brownie was [latex]480[/latex] calories, and had [latex]240[/latex] calories of fat. What percent of the total calories in each brownie comes from fat?

Answer: Solution

What are you asked to find? the percent of the total calories from fat
Choose a variable to represent it. Let [latex]p=[/latex] percent from fat.
Write a sentence that gives the information to find it. What percent of [latex]480[/latex] is [latex]240[/latex]?
Translate the sentence into an equation. .
Divide both sides by [latex]480[/latex]. .
Simplify. [latex]p=0.5[/latex]
Convert to percent form. [latex]p=\text{50%}[/latex]
Check. Is this answer reasonable?
Yes. [latex]240[/latex] is half of [latex]480[/latex], so [latex]50\text{%}[/latex] makes sense.
Write a complete sentence that answers the question. Of the total calories in each brownie, [latex]50\text{%}[/latex] is fat.

 

try it

[ohm_question]146703[/ohm_question]  
The following video show another example of how to solve an application that involves percent. https://youtu.be/mRekG7LsUys  

Licenses & Attributions

CC licensed content, Original

  • Question ID 146703, 146702, 146701, 146697. Authored by: Lumen Learning. License: CC BY: Attribution.

CC licensed content, Shared previously

  • Percent Application - Tipping. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
  • Example 1: Percent Application Problem. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.

CC licensed content, Specific attribution