Multi-Part Lesson
6-3
Applying Percents
PART
A
B
C
D
E
F
Percent of Change
Main Idea
Use bar diagrams
to solve problems
involving percent
of change.
NGSSS
MA.7.A.1.2 Solve
percent problems,
including problems
involving discounts,
simple interest, taxes, tips
and percents of increase
or decrease.
glencoe.com
ADMISSION The admission price for the state fair has increased by
50% in the last five years. If the admission price was $6 five years
ago, what is the current admission price?
What do you need to find? current admission price for the state
fair after a 50% increase
Draw a bar diagram that will represent 100%. Cut it out
and label it.
price 5 years ago = $6
100%
Draw a second bar diagram that is half the length of
the first. It represents 50%. Cut it out and label it.
increase = $3
50%
Tape the two bars together, end to end. This new bar
represents a 50% increase or 150% of the first bar.
price 5 years ago = $6
increase = $3
150%
The current admission price for the state fair is $6 + $3 or $9.
the Results
1. Suppose the price had increased 10%. What would you do
differently in Step 2? What is the new admission price?
2. Describe how this process would change to show percent of
decrease.
and Apply
3. Model each percent of change with bar diagrams.
a. 25% increase b. 75% increase c. 30% decrease d. 40% decrease
Lesson 6-3 Applying Percents
325
Multi-Part Lesson
6-3
Applying Percents
PART
A
Main Idea
Find the percent of
increase or decrease.
NGSSS
B
C
D
E
F
Percent of Change
FOOTBALL The table shows about how many people attended the
home games of a high school football team for five consecutive years.
MA.7.A.1.2 Solve
percent problems,
including problems
involving discounts,
simple interest, taxes, tips
and percents of increase
or decrease.
Attendance of Home Games
Year
Total Attendance
(thousands)
2007
16.6
2008
16.4
New Vocabulary
2009
16.9
percent of change
percent of increase
percent of decrease
2010
17.4
2011
17.6
1. How much did the attendance increase from 2009 to 2010?
glencoe.com
amount of increase
2. Write the ratio __
. Then write the ratio as
attendance in 2009
a percent. Round to the nearest hundredth.
3. How much did the attendance increase from 2008 to 2009?
amount of increase
4. Write the ratio __
. Then write the ratio as
attendance in 2008
a percent. Round to the nearest hundredth.
5. MAKE A CONJECTURE Why are the amounts of increase the same but
the percents different?
When you subtracted the original amount from the final amount, you
found the amount of change. When you compared the change to the
original amount in a ratio, you found the percent of change.
Percent of Change
Words
Equation
A percent of change is a ratio that compares the change in
quantity to the original amount.
amount of change
percent of change = __
orginal amount
final amount - original amount
= ___
original amount
When the percent of change is positive, then it is called a percent of
increase. When the percent of change is negative, then it is called a
326
Chapter 6 Percents
Find Percent of Increase
1970
GASOLINE Find the percent of
change in the cost of gasoline from
1970 to 2008. Round to the nearest
whole percent if necessary. Then
state whether the percent of change
is an increase or decrease.
2008
GAS
1.3 0
$
GAS
3 .9 5
$
Step 1 Find the amount of change.
$3.95 - $1.30 = $2.65
Step 2 Find the percent of change.
amount of change
original amount
$2.65
= _ Substitution
$1.30
percent of change = __
≈ 2.04
Percents
In the percent of change
formula, the decimal
repesenting the percent of
change must be written as
a percent.
Simplify.
≈ 204% Write 2.04 as a percent.
The percent of change is 204%. Since the percent of change is
positive, this is a percent of increase.
a. MEASUREMENT Find the percent of change from 10 yards to
13 yards.
Find Percent of Decrease
DVD RECORDER Yusuf bought a DVD recorder for $280. Now, it is
on sale for $220. Find the percent of change in the price. Round
to the nearest whole percent if necessary. Then state whether the
percent of change is an increase or decrease.
Step 1 Find the amount of change.
$220 - $280 = -$60
Step 2 Find the percent of change.
amount of change
original amount
-$60
= _ Substitution
$280
percent of change = __
≈ -0.21
Simplify.
≈ -21%
Write -0.21 as a percent.
The percent of change is -21%. Since the percent of change is
negative, this is a percent of decrease.
b. MONEY Find the percent of change from $20 to $15.
Lesson 6-3 Applying Percents
327
Examples 1 and 2
(p. 327)
Find each percent of change. Round to the nearest whole percent if
necessary. State whether the percent of change is an increase or a decrease.
1. 30 inches to 24 inches
2. 20.5 meters to 35.5 meters
3. $126 to $150
4. $75.80 to $94.75
5. SOCCER The table shows the number of youth
7 years and older who played soccer from 2000
to 2007.
a. Find the percent of change from 2004 to
2007. Round to the nearest tenth of a percent.
Is it a change of increase or decrease?
b. Find the percent of change from 2002 to
2004. Round to the nearest tenth of a percent.
Is it a change of increase or decrease?
Playing Soccer
Year
Number (millions)
2000
12.9
2002
13.7
2004
13.3
2006
14.0
2007
13.8
= Step-by-Step Solutions begin on page R15.
Extra Practice is on page EP16.
Examples 1 and 2
(p. 327)
Find each percent of change. Round to the nearest whole percent if
necessary. State whether the percent of change is an increase or a decrease.
6. 15 yards to 18 yards
7. 100 acres to 140 acres
8. $12 to $6
9. 48 notebooks to 14 notebooks
10. 125 centimeters to 87.5 centimeters 11 $15.60 to $11.70
12. 1.6 hours to 0.95 hour
13. 132 days to 125.4 days
14. $240 to $320
15. 624 feet to 702 feet
Find each percent of change. Round to the nearest whole percent if
necessary. State whether the percent of change is an increase or a decrease.
16. BOOKS On Monday, Kenya spent 60 minutes reading her favorite book.
Today, she spent 45 minutes reading this book.
17. EXERCISE Three months ago, Santos could walk 2 miles in 40 minutes.
Today he can walk 2 miles in 25 minutes.
18. SCHOOL Last school year the enrollment of Genoa Middle School was
465 students. This year the enrollment is 525.
19. MONEY Jake had $782 in his checking account. He now has $798.
20. MEASUREMENT Refer to the rectangle at the right.
Suppose the side lengths are doubled.
a. Find the percent of change in the perimeter.
b. Find the percent of change in the area.
328
Chapter 6 Percents
4 in.
2 in.
21. FIND THE DATA Refer to the Data File on pages 2–5. Choose some data
and write a real-world problem in which you would find the percent
of change.
Drop in CD Sales
2008
283 million
Year
22. SALES Use the graphic shown to
find the percent of change in CD
sales from 2008 to 2009.
2009
23 SHOES In 2010, shoe sales for a
certain company were $25.9 billion.
Sales are expected to increase by
about 20% from 2010 to 2011. Find
the projected amount of shoe sales in 2011.
271 million
270 275 280 285 290
Sale of CDs (in millions)
24. BABYSITTING The table shows how many hours
Catalina spent babysitting during the months of
April and May.
a. If Catalina charges $6.50 per hour, what is the
percent of change in the amount of money earned
from April to May? Is it a change of increase or
decrease?
Month
Hours
Worked
April
40
May
32
June
42
b. What is the percent of change in the amount of money earned from
May to June? Round to the nearest percent if needed. Is it a change of
increase or decrease?
c. Compare the percent of change from April to May and then May to
June. Which is a greater percent of change?
C
25. NUMBER SENSE The costs of two different sound systems were decreased
by $10. The original costs of the systems were $90 and $60, respectively.
Without calculating, which had a greater percent of decrease? Explain.
26. FIND THE ERROR Dario is finding the percent of
change from $52 to $125. Find his mistake and
correct it.
$125 - $52
__
≈ 0.58
$125
or 58%
27.
Explain how, when comparing data, two amounts of
change can be the same but the percents of change can be different.
Lesson 6-3 Applying Percents
329
NGSSS Practice
MA.7.A.1.2
28. Which of the following represents the
least percent of change?
30. Students in a reading program gradually
increased the amount of time they read.
The first week, they read 20 minutes per
day. Each week thereafter, they
increased their reading time by 50%
until they read an hour per day. In what
week of the program did the students
begin reading an hour per day?
A. A coat that was originally priced at
$90 is now $72.
B. A puppy who weighed 6 ounces at
birth now weighs 96 ounces.
C. A child grew from 54 inches to
60 inches in 1 year.
D. A savings account increased from
$500 to $550 in 6 months.
29.
31.
SHORT RESPONSE A music video
Web site received 5,000 comments on a
new song they released. After the artist
performed the song on television, the
number of comments increased by 30%
the next day. How many new comments
were on the Web site at the end of the
next day?
F. Week 2
H. Week 4
G. Week 3
I.
Week 5
GRIDDED RESPONSE Find the
percent of change in the perimeter of the
square below if its side length is tripled.
3 cm
3 cm
32. SURVEY There are 622 students at Jackson Middle School. About 52.3% of
them selected art class as their favorite class. What is a reasonable estimate
for the number of students who chose art as their favorite? (Lesson 6-2D)
ALGEBRA Write an equation for each problem. Then solve. Round to the
nearest tenth if necessary. (Lesson 6-2C)
33. 30% of what number is 17?
34. What is 21% of 62?
35. SHOPPING Four pounds of pecans cost $12.75. How much is this per
pound? (Lesson 4-1B)
36. MODELS On a scale model of a building,
3 inches = 12 feet. If the model is 8 inches tall,
how tall is the actual building? (Lesson 4-2B)
Multiply.
(Lesson 2-3B)
1
37. _
· 60
3
38. _
· 28
2
4
Add or subtract.
(Lesson 2-2D)
3
3
39. 3_
- 1_
8
330
4
Chapter 6 Percents
6
1
40. 7_
+ 1_
7
2
8 in.
Multi-Part Lesson
6-3
Applying Percents
PART
Main Idea
Solve problems
involving sales tax
and tips.
NGSSS
MA.7.A.1.2 Solve
percent problems,
including problems
involving discounts,
simple interest, taxes, tips
and percents of increase or
decrease. Also addresses
MA.7.A.3.2, MA.7.A.5.1.
A
B
C
D
E
F
Sales Tax and Tips
KAYAKS Alonso plans to buy a
new kayak that costs $1,849.
He lives in Florida where
there is a 7.5% sales tax.
1. Calculate the sales tax by
finding 7.5% of $1,849. Round
to the nearest cent.
2. What will be the total cost including the sales tax?
3. Multiply 1.075 and 1,849. How does the result compare to your
answer in Exercise 2?
New Vocabulary
sales tax
tip
gratuity
Sales tax is an additional amount of money charged on items that people
buy. The total cost of an item is the regular price plus the sales tax.
Find the Total Cost
glencoe.com
ELECTRONICS A DVD player costs $140 and the sales tax is 5.75%.
What is the total cost of the DVD player?
Method 1
Add sales tax to the regular price.
First, find the sales tax.
5.75% of $140 = 0.0575 × 140 Write 5.75% as a decimal.
= 8.05
The sales tax is $8.05.
Next, add the sales tax to the regular price.
$8.05 + $140 = $148.05
Method 2 Add the percent of tax to 100%.
100% + 5.75% = 105.75%
Add the percent of tax to 100%.
The total cost is 105.75% of the regular price.
105.75% of $140 = 1.0575 × $140
= $148.05
Write 105.75% as a decimal.
Multiply.
The total cost of the DVD player is $148.05.
a. CLOTHES What is the total cost of a sweatshirt if the regular
1
price is $42 and the sales tax is 5_
%?
2
Lesson 6-3 Applying Percents
331
A tip or gratuity is a small amount of money in return for a service.
The total price is the regular price of the service plus the tip.
Find the Tip
TIPPING A customer wants to tip 15% of
the restaurant bill. What will be the total
bill with tip?
Method 1
Add the tip to the regular price.
First, find the tip.
Real-World Link
In a recent year, the
Internal Revenue
Service estimated
that Americans paid
$15.37 billion in tips.
15% of $35 = 0.15 × 35
= 5.25
Write 15% as a decimal.
The tip is $5.25.
$5.25 + $35 = $40.25
Add the tip to the bill.
SAL’S BISTRO
Check 004322
5"#-&
8"*5&3
5*.&
%"5&
/6.#&3
Herbed Salmon
Chicken Pasta
Iced Tea
Iced Tea
$0%&
16.25
15.25
1.75
1.75
Total 35.00
THANK YOU
Method 2 Add the percent of tip to 100%.
100% + 15% = 115%
Add the percent of tip to 100%.
The total cost is 115% of the bill.
115% of $35 = 1.15 × $35 Write 115% as a decimal.
= $40.25
Multiply.
The total cost of the bill with tip is $40.25.
b. TAXICAB Scott wants to tip his taxicab driver. If his commute
costs $15 and he wants to give the driver a 20% tip, what is the
total cost?
HAIRCUTS A haircut costs $20. Sales tax is 4.75%. Is $25 sufficient to
cover the haircut with tax and a 15% tip?
Sales tax is 4.75% and the tip is 15%, so together they will be 19.75%.
Mental Math 10% of a
number can be found by
moving the decimal one
place to the left.
10% of $20 is $2. So,
20% of $20 is $4.
19.75% of $20 = 0.1975 × 20 Write 19.75% as a decimal.
= 3.95
$20 + $3.95 = $23.95
Multiply.
Add.
Yes, $25 is sufficient to cover the haircut with tax and tip.
c. SPA Find the total cost of a spa treatment of $42 including 6%
tax and 20% tip.
332
Chapter 6 Percents
Examples 1 and 2
(pp. 331–332)
Example 3
(p. 332)
Find the total cost to the nearest cent.
1. $2.95 notebook; 5% tax
2. $46 shoes; 2.9% tax
3. $28 lunch; 15% tip
4. $98 catered dinner; 18% gratuity
5. MANICURE Jaimi went to have a manicure that cost $30. She wanted to tip
the technician 20% and tax is 5.75%. How much did she spend total for
the manicure?
= Step-by-Step Solutions begin on page R16.
Extra Practice is on page EP16.
Examples 1 and 2
(pp. 331–332)
Example 3
(p. 332)
Find the total cost to the nearest cent.
6. $58 bill; 20% tip
7
8. $99 CD player; 5% tax
9. $13 haircut; 15% tip
$1,500 computer; 7% tax
10. $43 dinner; 18% gratuity
11. $7.50 meal; 6.5% tax
12. $39 pizza order; 15% tip
1
13. $89.75 scooter; 7_
% tax
4
14. PET GROOMING Toru takes his dog to be groomed. The fee to groom the
dog is $75 plus 6.75% tax. Is $80 enough to pay for the service? Explain.
15. CLEANING Diana and Sujit clean homes for a summer job. They charge
$70 for the job plus 5% for supplies. A homeowner gave them a 15% tip.
How much did they receive for the job?
16. VIDEO GAMES What is the sales tax of a $178.90 video game system if the
tax rate is 5.75%?
17 RESTAURANTS A restaurant bill comes to $28.35. Find the total cost if the
tax is 6.25% and a 20% tip is left on the amount before tax.
B
18. GRAPHIC NOVEL Refer to the graphic novel frame below. Find the price
that a student would pay including the group discount for each
amusement park. Which is the best deal?
We are trying
to find the
cheapest
admission
for our trip.
Refer to the
calculations
you made on
p. 303.
Lesson 6-3 Applying Percents
333
C
19. CHALLENGE The Leather Depot buys a coat from a supplier for $90
wholesale and marks up the price by 40%. What is the retail price
including 7% tax?
20. OPEN ENDED Give an example of the regular price of an item and the
total cost including sales tax if the tax rate is 5.75%.
21. Which One Doesn’t Belong? In each pair, the first value is the regular price
of an item and the second value is the price with gratuity. Identify the
pair that does not belong with the other three. Explain.
$30, $34.50
22.
NGSSS Practice
$54, $64.80
$16, $18.40
$90, $103.50
Describe two methods for finding the total price of a
bill that includes a 20% tip. Which method do you prefer? Explain.
MA.7.A.1.2
23. Ms. Taylor bought a water tube to pull
behind her boat. The tube cost $87.00
and 9% sales tax was added at the
register. Ms. Taylor gave the cashier five
$20 bills. How much change should she
have received?
A. $4.83
B. $5.17
24. Prices for several cell phones are listed
in the table below. It shows the regular
price p and the price with tax t.
Regular Price (p)
Price with Tax (t)
Flip phone
Phone
$80
$86.40
Slide phone
$110
$118.80
Picture phone
$120
$129.60
Which formula can be used to calculate
the price with tax?
C. $94.83
D. $117.00
F. t = p × 0.8
H. t = p × 0.08
G. t = p - 0.8
I.
t = p × 1.08
Find each percent of change. Round to the nearest whole percent if necessary.
State whether the percent of change is an increase or decrease. (Lesson 6-3B)
25. 4 hours to 6 hours
26. $500 to $456
27. 20.5 meters to 35.5 meters
28. FINANCIAL LITERACY Bethany has to pay a 20% handling fee on a book she
ordered online that cost $12. Write and solve a percent equation to find the
handling fee. (Lesson 6-2C)
Multiply. Write in simplest form.
2 _
29. _
·4
7
334
5
Chapter 6 Percents
(Lesson 2-3B)
1 _
30. _
·4
8
9
6 _
31. _
· 9
11
24
Multi-Part Lesson
6-3
Applying Percents
PART
Main Idea
Solve problems
involving discount.
NGSSS
MA.7.A.1.2 Solve
percent problems,
including problems
involving discounts,
simple interest, taxes, tips
and percents of increase
or decrease. Also
addresses MA.7.A.3.2,
MA.7.A.5.1.
New Vocabulary
discount
A
B
C
D
E
F
Discount
WATER PARKS A pass at a water park
is $58. Halfway through the season,
the pass is discounted by 20%.
1. Calculate the discount by finding
20% of $58. Round to the
nearest cent.
2. What will be the discounted price?
3. Multiply 0.8 and $58. How does the result compare to your answer
in Exercise 2?
Discount is the amount by which the regular price of an item is
reduced. The sale price is the regular price minus the discount.
glencoe.com
DVDs A DVD normally costs $22. This week it is on sale for 25%
off the original price. What is the sale price of the DVD?
Method 1
Subtract the discount from the regular price.
First, find the amount of the discount.
25% of $22 = 0.25 × $22 Write 25% as a decimal.
= $5.50
The discount is $5.50.
Next, subtract the discount from the regular price.
$22 - $5.50 = $16.50
Method 2 Subtract the percent of discount from 100%.
100% - 25% = 75%
Subtract the discount from 100%.
The sale price is 75% of the regular price.
75% of $22 = 0.75 × $22 Write 75% as a decimal.
= $16.50
Multiply.
The sale price of the DVD is $16.50.
a. CLOTHES A shirt is regularly priced at $42. It is on sale for 15%
off. What is the sale price of the shirt?
Lesson 6-3 Applying Percents
335
Find the Sale Price
BOOGIE BOARDS A boogie board that has a regular price of $69 is
on sale at a 35% discount. What is the sale price with 7% tax?
Sales Tax and Discount
If both are represented as
percents, sales tax is a
percent of increase and
discount is a percent of
decrease.
Step 1 Find the amount of the discount.
35% of $69 = 0.35 · $69 Write 35% as a decimal.
= $24.15
The discount is $24.15.
Step 2 Subtract the discount from the regular price.
$69 - $24.15 = $44.85
Step 3 The percent of tax is applied after the discount is taken.
7% of $44.85 = 0.07 · 44.85
Write 7% as a decimal.
= 3.14
The tax is $3.14.
Add the tax to the sale price of the boogie board.
$44.85 + $3.14 = $47.99
The sale price of the boogie board including tax is $47.99.
b. MUSIC A CD that has a regular price of $15.50 is on sale at a
25% discount. What is the sale price with 6.5% tax?
Find the Original Price
CELL PHONES A cell phone is on sale for 30% off. If the sale price
is $239.89, what is the original price?
The sale price is 100% - 30% or 70% of the original price.
Words
Percent Equation
Remember that in the
percent equation, the
percent must be written as
a decimal. Since the sale
price is 70% of the original
price, use 0.7 to represent
70% in the percent
equation.
$239.89 is 70% of what price?
Variable
Let p represent the original price.
Equation
$239.89 = 0.7
×
p
BACK
239.89 = 0.7p
_ _
Write the equation.
0.7p
239.89
=
0.7
0.7
Divide each side by 0.7.
342.70 = p
Simplify.
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TALK
1
4
7
GHI
PQRS
Shift
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ABC
JKL
END
2
5
8
+ 0
TUV
DEF
3
MNO
6
9
#
Z
WYX
e
Spac
The original price is $342.70.
c. Find the original price if the sale price of the cell phone is $205.50.
336
Chapter 6 Percents
Example 1
(p. 335)
Example 2
(p. 336)
Example 3
(p. 336)
Find the sale price to the nearest cent.
1. $210 bicycle; 25% discount
2. $40 sweater; 33% discount
3. $1,575 computer; 15% discount; 4.25% tax
4. $119.50 skateboard; 20% off; 7% tax
5. IN-LINE SKATES A pair of in-line skates is on sale for $90. If this price
represents a 9% discount from the original price, what is the original
price to the nearest cent?
= Step-by-Step Solutions begin on page R16.
Extra Practice is on page EP16.
Examples 1 and 2
(pp. 335–336)
Find the sale price to the nearest cent.
6. $64 jacket; 20% discount
7. $1,200 TV; 10% discount
8. $199 MP3 player; 15% discount
9. $12.25 pen set; 60% discount
10. $4.30 makeup; 40% discount; 6% tax
11 $7.50 admission; 20% off; 5.75% tax
12. $39.60 sweater; 33% discount; 4.5% tax
1
13. $90.00 skateboard; 33_
% off; 8% tax
3
Example 3
(p. 336)
14. COSMETICS A bottle of hand lotion is on sale for $2.25. If this price
represents a 50% discount from the original price, what is the original
price to the nearest cent?
15. TICKETS At a movie theater, the cost of admission to a matinee is $5.25.
If this price represents a 30% discount from the evening price, find the
evening price to the nearest cent.
Find the original price to the nearest cent.
16. calendar: discount, 75%
sale price, $2.25
B
17. telescope: discount, 30%
sale price, $126
18. COMPUTERS The Wares want to buy a new computer. The regular price is
$1,049. The store is offering a 20% discount and a sales tax of 5.25% is
added after the discount. What is the total cost?
19
MULTIPLE REPRESENTATIONS An online
store is having a sale on digital cameras.
The table shows the regular price and the
sale price for the cameras.
a. TABLE Copy the table including a column
for the discount.
Camera
Model
Regular
Price
Sale
Price
A
$97.99
$83.30
B
$102.50
$82.00
C
$75.99
$65.35
D
$150.50
$135.45
b. WORDS Write a verbal rule that can be
used to find the percent of decrease for
any of the cameras.
c. NUMBERS Which model has the best discount?
Lesson 6-3 Applying Percents
337
C
20. CHALLENGE A gift store is having a sale in which all items are
discounted 20%. Including tax, Colin paid $21 for a picture frame.
If the sales tax rate is 5%, what was the original price of the picture
frame?
21. OPEN ENDED Give an example of the sale price of an item and the total
cost including sales tax if the tax rate is 5.75% and the item is 25% off.
22. REASONING Two department stores, The James Store and Ratcliffe’s, are
having sales. The stores sell the same brand of sneakers. The James
Store usually sells them for $50, but has marked them at 40% off. At
Ratcliffe’s, the sneakers are marked down to 30% off of the usual price
of $30. Which store has the better sale price? Explain.
23.
NGSSS Practice
Describe two methods for finding the sale price of an
item that is discounted 30%. Which method do you prefer? Explain.
MA.7.A.1.2
24. A computer software store is having a
sale. The table shows the regular price r
and the sale price s of various items.
Item
Regular Price (r)
Sale Price (s)
A
$5.00
$4.00
B
$8.00
$6.40
C
$10.00
$8.00
D
$15.00
$12.00
Which formula can be used to calculate
the sale price?
A. s = r × 0.2
C. s = r × 0.8
B. s = r - 0.2
D. s = r - 0.8
25. A chair that costs $210 was reduced by
40% for a one-day sale. After the sale,
the sale price was increased by 40%.
What is the price of the chair?
F. $176.40
H. $205.50
G. $185.30
I.
$210.00
26. Carmen paid $10.50 for a T-shirt at the
mall. It was on sale for 30% off. What
was the original price before the
discount?
A. $3.15
C. $15.00
B. $7.35
D. $35.00
27. RESTAURANTS Mitchell spent $13 on dinner. He wants to tip the server 15%.
About how much money should he leave as the tip? (Lesson 6-3C)
Find the percent of change. Round to the nearest whole percent if necessary.
State whether the percent of change is an increase or decrease. (Lesson 6-3B)
28. 35 birds to 45 birds
338
Chapter 6 Percents
29. 60 inches to 38 inches
30. $2.75 to $1.80
Multi-Part Lesson
6-3
Applying Percents
PART
Main Idea
Solve problems
involving simple
interest.
NGSSS
MA.7.A.1.2 Solve
percent problems,
including problems
involving discounts,
simple interest, taxes, tips
and percents of increase or
decrease. Also addresses
MA.7.A.3.2.
New Vocabulary
principal
simple interest
A
B
C
E
D
F
Financial Literacy: Simple Interest
INVESTING Suni plans to save the
$200 she received for her birthday.
The table shows the average yearly
rates at three different banks.
Bank
Nation Bank
1. Calculate 2.50% of $200 to find the
amount of money Suni can earn in
one year at Federal Credit Union.
Interest
Rate
3%
Federal Credit Union
2.50%
First Bank
2.75%
2. Calculate 2.75% of $200 to find the amount of
money Suni can earn in one year at First Bank.
Principal is the amount of money deposited or borrowed. Simple
interest is the amount paid or earned for the use of money. To find
simple interest I, use the following formula.
Annual interest rate,
written as a decimal.
Interest
glencoe.com
=
Principal
Time, expressed in years.
Find Interest Earned
CHECKING Arnold has $580 in a savings account that pays 3%
interest. How much interest will he earn in each amount of time?
5 years
I = prt
Formula for simple interest
I = 580 · 0.03 · 5 Replace p with $580, r with 0.03, and t with 5.
I = 87
Simplify.
Arnold will earn $87 in interest in 5 years.
6 months
6
6 months = _
or 0.5 year Write the time as years.
12
I = prt
Formula for simple interest
I = 580 · 0.03 · 0.5
p = $580, r = 0.03, t = 0.5
I = 8.7
Simplify.
Arnold will earn $8.70 in interest in 6 months.
Lesson 6-3 Applying Percents
339
a. SAVINGS Jenny has $1,560 in a savings account that pays 2.5%
simple interest. How much interest will she earn in 3 years?
The formula I = prt can also be used to find the interest owed when
you borrow money. In this case, p is the amount of money borrowed
and t is the amount of time the money is borrowed.
Find Interest Paid on a Loan
LOANS Rondell’s parents borrow $6,300 from the bank for a new
car. The interest rate is 6% per year. How much simple interest
will they pay if they take 2 years to repay the loan?
Real-World Link
There are over
250 million registered
passenger vehicles in
the United States.
I = prt
Formula for simple interest
I = 6,300 · 0.06 · 2
Replace p with $6,300, r with 0.06, and t with 2.
I = 756
Simplify.
Rondell’s parents will pay $756 in interest in 2 years.
b. LOANS Mrs. Hanover borrows $1,400 at a rate of 5.5% per year.
How much simple interest will she pay if it takes 8 months to
repay the loan?
Find Total Paid on a Credit Card
CREDIT CARDS Derrick’s dad bought new tires for $900 using a
credit card. His card has an interest rate of 19%. If he has no other
charges on his card and does not make a payment, how much
money will he owe after one month?
I = prt
Fractions of Years
Remember to express
1
1 month as _
12 year in the
formula.
_
Formula for simple interest
I = 900 · 0.19 · 1
Replace p with $900, r with 0.19, and t with _.
I = 14.25
Simplify.
12
1
12
The interest owed after one month is $14.25. So, the total amount
owed would be $900 + $14.25 or $914.25.
c. CREDIT CARDS An office manager charged $425 worth of office
supplies on a credit card with an interest rate of 9.9%. How much
money will he owe at the end of the month if he makes no other
charges on the card and does not make a payment?
340
Chapter 6 Percents
Examples 1 and 2
(pp. 339–340)
Example 3
(p. 340)
Find the simple interest earned to the nearest cent for each principal,
interest rate, and time.
1. $640, 3%, 2 years
2. $1,500, 4.25%, 4 years
3. $580, 2%, 6 months
4. $1,200, 3.9%, 8 months
Find the simple interest paid to the nearest cent for each loan, interest rate,
and time.
5
Example 4
(p. 340)
$4,500, 9%, 3.5 years
6. $290, 12.5%, 6 months
7. FINANCES The Masters family financed a computer that cost $1,200. If the
interest rate is 19%, how much will the family owe for the computer after
one month if no payments are made?
= Step-by-Step Solutions begin on page R16.
Extra Practice is on page EP17.
Examples 1 and 2
(pp. 339–340)
Find the simple interest earned to the nearest cent for each principal,
interest rate, and time.
8. $1,050, 4.6%, 2 years
10. $500, 3.75%, 4 months
Example 3
(p. 340)
Example 4
(p. 340)
9. $250, 2.85%, 3 years
11. $3,000, 5.5%, 9 months
Find the simple interest paid to the nearest cent for each loan, interest rate,
and time.
12. $1,000, 7%, 2 years
13. $725, 6.25%, 1 year
14. $2,700, 8.2%, 3 months
15. $175.80, 12%, 8 months
16. CREDIT CARDS Leon charged $75 at an interest rate of 12.5%. How much
will Leon have to pay after one month if he makes no payments?
17. TRAVEL A family charged $1,345 in travel expenses to a credit card with a
7.25% interest rate. If no payments are made, how much will they owe
after one month for their travel expenses?
B
18. BANKING The table shows interest rates
that can be earned for various lengths
of time.
Home Savings and Loan
a. What is the simple interest earned on
$900 for 9 months?
b. Find the simple interest earned on
$2,500 for 18 months.
Time
Rate
6 months
9 months
12 months
18 months
2.4%
2.9%
3.0%
3.1%
19 INVESTING Ramon has $4,200 to invest for college.
a. If Ramon invests $4,200 for 3 years and earns $630, what is the simple
interest rate?
b. Ramon’s goal is to have $5,000 after 4 years. Is this possible if he
invests with a rate of return of 6%? Explain.
Lesson 6-3 Applying Percents
341
C
20. OPEN ENDED Suppose you earn 3% on a $1,200 deposit for 5 years.
Explain how the simple interest is affected if the rate is increased by 1%.
What happens if the time is increased by 1 year?
21. CHALLENGE Mrs. Antil deposits $800 in a savings account that earns
3.2% interest annually. At the end of the year, the interest is added to
the principal or original amount. She keeps her money in this account
for three years without withdrawing any money. Find the total in her
account after each year for three years.
22.
NGSSS Practice
List the steps you would use to find the simple
interest on a $500 loan at a 6% interest rate for 18 months. Then find
the simple interest.
MA.6.A.3.2, MA.7.A.1.2
23. Jada invests $590 in a money market
account. Her account pays 7.2% simple
interest. If she does not add or withdraw
any money, how much interest will
Jada’s account earn after 4 years of
simple interest?
24. Mr. Sprockett borrows $3,500 from his
bank to buy a used car. The loan has a
7.4% annual simple interest rate. If it
takes Mr. Sprockett two years to pay
back the loan, what is the total amount
he will be paying?
A. $75.80
F. $3,012
B. $158.67
G. $3,598
C. $169.92
H. $4,018
D. $220.67
I.
$4,550
25. SPORTS Find the total cost of a $20 volleyball if it is on sale for 33% off.
(Lesson 6-3D)
Find the total cost of each of the following.
(Lesson 6-3C)
26. backpack, $25 with 7% tax
1
27. car, $8,000 with 5_
% tax
2
28. dinner, $50 with 18% tip
29. car wash, $25 with 15% tip
Divide. Write in simplest form.
(Lesson 2-3D)
3
1
30. _
÷_
5
4
31. _
÷_
5
342
2
Chapter 6 Percents
7
8
2
1
32. 2_
÷ 1_
3
4
Multi-Part Lesson
6-3
Applying Percents
PART
A
B
C
D
F
E
Spreadsheet:
Main Idea
Simple Interest
Use a spreadsheet to
calculate simple
interest.
A computer spreadsheet is a useful tool for quickly calculating simple
interest for different values of principal, rate, and time.
NGSSS
MA.7.A.1.2 Solve
percent problems,
including problems
involving discounts,
simple interest, taxes, tips
and percents of increase or
decrease.
SAVINGS Joel plans on opening a “Young Savers” account at his
bank. The current rate on the account is 4%. To find the balance
at the end of 2 years for different principal amounts, he enters
the values B2 = 4 and C2 = 2 into the spreadsheet below.
Simple Interest
A
glencoe.com
1
2
3
4
5
6
7
8
T
B
Principal (p)
500
1000
1500
2000
2500
Sheet 1
C
Rate (r)
=B2/100
=B2/100
=B2/100
=B2/100
=B2/100
Sheet 2
D
Time (t)
=C2
=C2
=C2
=C2
=C2
E
Interest (I)
=A3*B3*C3
=A4*B4*C4
=A5*B5*C5
=A6*B6*C6
=A7*B7*C7
New Balance
=A3+D3
=A4+D4
=A5+D5
=A6+D6
=A7+D7
Sheet 3
For each principal given in column A, simple
interest is calculated for any values of rate and
time entered in B2 and C2, respectively.
The spreadsheet
adds simple interest
to the principal.
the Results
1. Why is the rate in column B divided by 100?
2. What is the balance in Joel’s account after 2 years if the principal
is $1,500 and the simple interest rate is 4%?
3. How much interest does Joel earn in 2 years if his account has a
principal of $2,000 and a simple interest rate of 4%?
4. Is the amount of principal proportional to the interest Joel earns if
his account earns 4% simple interest over 2 years? Explain.
5. Is the amount of principal proportional to the balance in Joel’s
account if it earns 4% simple interest over 2 years? Explain.
Lesson 6-3 Applying Percents
343