# 6.2 Solve general applications of percent  (Page 2/7)

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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.

Dezohn and his girlfriend enjoyed a dinner at a restaurant, and the bill was $\text{68.50}.$ They want to leave an $\text{18%}$ tip. If the tip will be $\text{18%}$ 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 $t=$ 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. Check. Is this answer reasonable? If we approximate the bill to $70 and the percent to 20%, we would have a tip of$14. So a tip of $12.33 seems reasonable. Write a complete sentence that answers the question. The couple should leave a tip of$12.33.

Cierra and her sister enjoyed a special dinner in a restaurant, and the bill was $\text{81.50}.$ If she wants to leave $\text{18%}$ of the total bill as her tip, how much should she leave?

$14.67 Kimngoc had lunch at her favorite restaurant. She wants to leave $\text{15%}$ of the total bill as her tip. If her bill was $\text{14.40},$ how much will she leave for the tip?$2.16

The label on Masao's breakfast cereal said that one serving of cereal provides $85$ milligrams (mg) of potassium, which is $\text{2%}$ of the recommended daily amount. What is the total recommended daily amount of potassium?

## Solution

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

One serving of wheat square cereal has $7$ grams of fiber, which is $\text{29%}$ of the recommended daily amount. What is the total recommended daily amount of fiber?

24.1 grams

One serving of rice cereal has $190$ mg of sodium, which is $\text{8%}$ of the recommended daily amount. What is the total recommended daily amount of sodium?

2,375 mg

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

## Solution

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

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