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
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
Base
Multiply each side by
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 0.42
n = 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)
30
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
Example 3: Find the Base
83.5 is 125% of what number?
You know that the part is 83.5 and the percent
Is 125. Let n represent the base.
Part = Percent Base
83.5 = 1.25n
83.5 = 1.25n
1.25 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 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 = 1.2125 Since this is money, round to the nearest hundredth
D = 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 $$ so round to
nearest hundredth!
The sale price of the pizza will be $3.64
Simple Interest
Use the following formula:
Annual Interest Rate (as a decimal)
Interest------>
I = prt <----- Time (in years)
principal (amt. of $$ invested/
borrowed)
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
456 = 9600r
9600 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 = Percentbase
A. 12 is what percent of 400?
12= P400
P= .03 move the decimal to make it a %
3%
B.
What is 20% of 110?
p = .20(110)
p = 22
C. 30 is 60% of what number?
30 = .60b
50 = 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?
D = .35(180)
D = 63
$180-$63 = $117
How long will it take to earn $252 in interest if
$2400 is invested at a 7% annual interest
rate?
I = prt
252= 2400(.07)t
252=168t
1.5 = t
It will take 1.5 years
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!