Solving Applications With 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, 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.

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].

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?

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.

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.

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