Chapter 6 Lesson 7Using Percent Equations

Pgs. 298-302

What you will learn:

Solve percent problems using percent equations

Solve real-life problems involving discount and interest

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

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

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

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 0.42n = 63 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.

Example 2: Find the Percent

37.5 is what percent of 30?

You know that the base is 30 and the part is 37.5. Let n represent the percent.

Part = Percent Base

37.5 = n(30)

37.5 = n(30) Divide each side by 30 30 30

1.25 = n Move the decimal 2 places left to change into a %

So, 37.5 is 125% of 30

Example 3: Find the Base83.5 is 125% of what number? You know that the part is 83.5 and the percentIs 125. Let n represent the base.

Part = Percent Base

83.5 = 1.25n

83.5 = 1.25n1.25 1.25 Remember, using the percent equation, the

percent is turned to a decimal.66.8 = n

So, 83.5 is 125% of 66.8

The percent equation can also be used to solve problems involving

discount and interest.

Example 4: Find DiscountA 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 = 1.2125 Since this is money, round to the nearest hundredthD = 1.21

Then find the sale price: $4.85 - $1.21 = $3.64

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 = 3.6375 Remember, dealing with $$ so round to

nearest hundredth!The sale price of the pizza will be $3.64

Simple InterestUse the following formula:

Interest------> I = prt <----- Time (in years)

principal (amt. of $$ invested/ borrowed)

Simple InterestUse the following formula:

Interest------> I = prt <----- Time (in years)

principal (amt. of $$ invested/ borrowed)

Annual Interest Rate (as a decimal)

Example 5: Apply Simple Interest Formula

I= prtWhat is the annual interest rate if $1600 is invested for

6 years and $456 in interest is earned?Fill in the formula!456 = 1600r6456 = 9600r456 = 9600r9600 9600

R = .0475 Turn the decimal into a percent So, the interest rate is 4.75%

Your Turn!Solve each problem using the percent equation. part = Percentbase

A. 12 is what percent of 400?

B. What is 20% of 110?

C. 30 is 60% of what number?

12= P400P= .03 move the decimal to make it a %

3%

p = .20(110)p = 22

30 = .60b50 = b

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 = prt252= 2400(.07)t252=168t1.5 = tIt will take 1.5 years

QUIZ TOMORROW over6-6 and 6-7

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