1. 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

2. 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

3. 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

4. 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

5. 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.

6. 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

7. 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

8. 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

9. 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

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

11. 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%

12. Your Turn. Solve each problem using the percent equation
Your Turn! Solve each problem using the percent equation. part = Percentbase
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

13. 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

14. 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!