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Published byMaximillian Briggs Modified over 4 years ago

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**Chapter 6 Lesson 7 Using Percent Equations Pgs. 298-302**

What you will learn: Solve percent problems using percent equations Solve real-life problems involving discount and interest

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Vocabulary Percent Equation (298): an equivalent form of the percent proportion in which the percent is written as a decimal Discount (299): the amount by which the regular price of an item is reduced Simple Interest (300): the amount of money paid or earned for the use of money

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**The Percent Equation Part = Percent <----The percent is**

Base written as a decimal Part Base = Percent Base Multiply each side by Base the base Part = Percent Base <-----this is the percent equation

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**Concept Summary: The Percent Equation**

Type Example Equation Missing Part What number is 75% of 4? n = 0.75(4) Missing Percent 3 is what percent of 4? 3 = n(4) Missing Base 3 is 75% of what number? 3 = 0.75n

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**Example 1: Find the Part Find 42% of 150**

You know the base is 150 and the percent is 42%. Let n represent the part. n = 0.42(150) Write 42% as the decimal 0.42 n = Simplify So, 42% of 150 is 63. Is that reasonable? Yes because you know that 75 is 50% of 150, so 42% should be less than half.

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**Example 2: Find the Percent**

37.5 is what percent of 30? You know that the base is 30 and the part is Let n represent the percent. Part = Percent Base 37.5 = n(30) 37.5 = n(30) Divide each side by 30 1.25 = n Move the decimal 2 places left to change into a % So, 37.5 is 125% of 30

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**Example 3: Find the Base 83.5 is 125% of what number?**

You know that the part is 83.5 and the percent Is Let n represent the base. Part = Percent Base 83.5 = 1.25n Remember, using the percent equation, the percent is turned to a decimal. 66.8 = n So, 83.5 is 125% of 66.8

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**Example 4: Find Discount**

The percent equation can also be used to solve problems involving discount and interest. Example 4: Find Discount A frozen pizza is on sale at a 25% discount. Find the sale price of the pizza if it normally sells for $4.85 Method 1: First use the percent equation to find 25% of $4.85 Let D = the discount Part = Percent Base D = .25(4.85) D = Since this is money, round to the nearest hundredth D = 1.21 Then find the sale price: $ $1.21 = $3.64

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**A frozen pizza is on sale at a 25% discount**

A frozen pizza is on sale at a 25% discount. Find the sale price of the pizza if it normally sells for $4.85 Method 2: A discount of 25% means the item will cost 100% - 25% or 75% of the original price. Use the percent equation to find 75% of $4.85 Let s represent the sale price. S = 0.75(4.85) S = Remember, dealing with $$ so round to nearest hundredth! The sale price of the pizza will be $3.64

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**Annual Interest Rate (as a decimal)**

Simple Interest Use the following formula: Interest------> I = prt <----- Time (in years) principal (amt. of $$ invested/ borrowed)

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**Example 5: Apply Simple Interest Formula I= prt**

What is the annual interest rate if $1600 is invested for 6 years and $456 in interest is earned? Fill in the formula! 456 = 1600r6 456 = 9600r 9600 R = Turn the decimal into a percent So, the interest rate is 4.75%

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**Your Turn. Solve each problem using the percent equation**

Your Turn! Solve each problem using the percent equation. part = Percentbase 12 is what percent of 400? What is 20% of 110? 30 is 60% of what number? 12= P400 P= move the decimal to make it a % 3% p = .20(110) p = 22 30 = .60b 50 = b

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2 More! A jacket that normally sells for $180 is on sale at a 35% discount. What is the sale price of the jacket? How long will it take to earn $252 in interest if $2400 is invested at a 7% annual interest rate? D = .35(180) D = 63 $180-$63 = $117 I = prt 252= 2400(.07)t 252=168t 1.5 = t It will take 1.5 years

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**QUIZ TOMORROW over 6-6 and 6-7**

Extra Practice by the door on your way out! Make sure you keep on top of this by reviewing everyday!

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