UNIT FOUR: Prealgebra in a Technical World
4.8 Solving Percents Using Proportions
SWBAT 1. Calculate answers to percent problems.
2. Use proportions to solve percent application problems.
3. Find and use percents of increase and decrease.
 Gabrielle has two scores on her test: 19 points and 79%. There were 10 problems on the
test, and she wonders what the total points for the test were.
 Colleen wants to keep her heart rate between 60% and 80% of her maximum while
exercising. Her maximum heart rate is 180 beats per minute.
 Jeremiah’s total family monthly income after college costs and day care deductions is
$3,740. The family mortgage and utilities are $1,890 per month. He sees the
recommendation that his housing costs should be about 44% of his budget. He wonders
how close he is to this recommendation.
Each of the problems above fits one of three types of percentage problems. Yet each
can be solved using the same type of proportion.
In this section we study how to use proportions to solve problems involving
percentages and how to think through multiple-step problems involving percentages.
Percents, Amounts, Base and Proportions
When we use a percent, we are always making a comparison. We compare how many
out of 100 is equal to a part of a whole something. We call this “whole something” the base.
We call the “part of the whole” the amount. For example, on a 50% off sale, we pay $30 for a
$60 item. Notice that 50 percent is 50 out of 100 which is equal to the amount of $30 when
50
30
compared to a base of $60. We can write this using the proportion 100 = 60.
397
398
SECTION 4.8 Solving Percents Using Proportions
Percent problems usually fall into one of three categories; we need to find the percent,
the base or the amount while the other two values are known. We can always write a
proportion to solve these problems. To do this we let the ratio,
𝑷
100
, represent the percentage,
where P % is a percent.
DEFINITION: For any percent problem we can write the proportion:
𝑷
𝑨
=
100 𝑩
that is
𝑷
𝑨𝑚𝑜𝑢𝑛𝑡
=
where 𝑷% is a percent.
100
𝑩𝑎𝑠𝑒
We use the variables 𝑨, 𝑩 and 𝑷 to name the value that is unknown. Use the table
below to become familiar with the English phrases that lead to a correct proportion for a
problem situation. Some people use the vertical scale to successfully set up proportions.
Phrases
Vertical Scale
Proportion & Solution
9 is what percent of 45?
𝑃
𝐴
= ,
100 𝐵
The percent is missing.
45 ∙ 𝑃 = 900,
𝑃
9
=
100 45
𝑃 = 20
9 is 20% of 45
𝑃
𝐴
= ,
100 𝐵
15% of $35 is what?
525 = 100 ∙ 𝐴,
The amount is missing.
𝐴 = 5.25
15% of $35 is 5.25
𝑃
𝐴
= ,
100 𝐵
42 is 5% of what?
5 ∙ 𝐵 = 4200,
The base is missing.
15
𝐴
=
100 35
𝐵
5
42
=
100
𝐵
𝐵 = 840
42 is 5% of 840
UNIT FOUR: Prealgebra in a Technical World
 Check Point 1
a. What percent of 75 is 27? ______________________________________________________
b. 32% of $4,000 is what? ________________________________________________________
c. 28 out of 70 is what percent? ___________________________________________________
d. 120 is 1.5% of what number? ___________________________________________________
Amounts correspond to the percentage and the Base always corresponds to 100 in the
𝑷→ → →
percent proportion equation,
100 → → →
=
𝑨𝑚𝑜𝑢𝑛𝑡
𝑩𝑎𝑠𝑒
. To keep from mixing these up, we make
sure we focus on the distinctions between the values for Amounts and Bases.
Example 1:
a. What percent is 50 out of 75?
Think it through: a. For “50 out of 75,” 50 is the Amount and 75 is the Base.
You are missing the percent, so find P.
50
70
Estimate first that 75 ≈ 100, so about 70%
𝑷
50
Write the proportion.
=
100 75
75𝑷 = 5,000 Use cross products and multiply.
5,000
𝑷 is the missing factor, so divide.
75
2
Use your calculator.
𝑷 = 66
3
𝑷=
2
66 3 % is the percent P % is a percent
2
66 3 % is about 70%. Our result is close to our estimate so it checks.
𝟐
ANSWER: 50 out of 75 is 𝟔𝟔 𝟑 %.
399
400
SECTION 4.8 Solving Percents Using Proportions
b. What percent is 75 out of 50?
Think it through: b. For “75 out of 50,” 75 is the Amount and 50 is the Base.
We are missing the percent.
𝟏𝟓𝟎
75
Using mental math 100 = 50, so 150% will be our answer.
We use a proportion to verify this.
𝑷
75
Write the proportion.
=
100 50
50𝑷 = 7,500 Use cross products and multiply.
𝑷=
7,500
𝑷 is the missing factor, so divide.
50
𝑷 = 150
Use mental math or your calculator.
150% is the percent P % is the percent.
Our answer is the same solving this problem two ways, so it checks.
ANSWER: 75 out of 50 is 𝟏𝟓𝟎%.
In Example 1b the Amount was more than the Base, which led to a percent value that
was more than 100%.

Check Point 2
Bubba is really confused now. He found a 70% off sale for a shrimp trawling net setup. He paid
$79.50 and decides to find how much the net would have cost originally. He knows he paid
30
𝐴
30%, so he writes: 100 = $79.5 , but when he uses cross multiplication and solves this correctly,
he comes up with $23.85. He knows he should not have to move the decimal point anywhere,
and even if he moves it two places left or right, these values are also not correct. How should
Bubba have calculated the original price for his shrimp trawling net?
UNIT FOUR: Prealgebra in a Technical World
Solving Percent Application Problems
We can take any percent application and rephrase it to determine what the percent,
base and amount are. While some people use this strategy most of the time, others prefer to
use the vertical scale to translate. Either way, learn both of these strategies just in case your
favorite strategy is not working on a certain problem.
In the last check point, Bubba at least recognized the unreasonableness of his answer.
Bubba also knew he could use a proportion to solve his percent problem. But Bubba did not
identify the Amount and Base of his proportion correctly. It is often useful to concentrate on
finding the Base, the amount that is 100%, first.
Example 2: Gabrielle has two scores on her test: 19 points and 79%. There were 10 problems
on the test. What point score would have given her 100%?
Think it through:
Understand: We rephrase the problem, “19 is 79% of what number?” We
are missing the Base.
Plan: Use a proportion to solve. Draw a vertical scale to
make sure we set up the correct proportion.
Solve: The percent is 79%, so P = 79. The amount is 19 and
we are looking for the base. Because 19 to 79 is about 20 to
80 and 20 to 80 is the same ratio as 25 to 100, estimate 𝐵 ≈
25 using scaling.
79
19
Write the proportion.
=
100
𝐵
79𝐵 = 1900 Use cross multiplication.
𝐵 = 1900 ÷ 79 𝐵 is a missing factor so divide.
𝐵 ≈ 24.0506 ≈ 24 Use a calculator and round to a reasonable answer.
Check: This fits our estimate of 𝐵 ≈ 25 points, so we accept this answer.
401
402
SECTION 4.8 Solving Percents Using Proportions
ANSWER: A score of 𝟐𝟒 points would have given Gabrielle 𝟏𝟎𝟎% . (Notice that when
working with percents, we often will have to round our results to
reasonable answers.)
Example 3: Colleen wants to keep her heart rate above 60% while exercising. Her maximum
heart rate is 180 beats per minute. What is this lowest acceptable heart rate?
Think it through:
Understand: We rephrase this problem, “What is 60% of 180?”
Plan: Use a proportion to solve. Draw a vertical scale to make
sure we set up the correct proportion.
Solve: The base is 180, the percent is 60% so P = 60, and we are
looking for the amount.
Estimate A ≈ 100 because 60/100 is about 100/180.
60
𝐴
Write the proportion.
=
100 180
10,800 = 100𝐴 Use cross products and multiply.
𝐴 = 108 Divide.
Check: 𝐴 = 108 fits our estimate of 𝐴 ≈ 100, so accept this answer.
ANSWER: Colleen should keep her heart rate above 108 beats per minute.
UNIT FOUR: Prealgebra in a Technical World
Example 4: Jeremiah’s total family monthly income after college costs and day care deductions
is $3,740. The family mortgage and utilities are $1,890 per month. How does this amount
compare to the 44% guideline for housing expenses?
Think it through:
Understand: We rephrase this question, “$1,890 is what percent of $3,740?”
Plan: Use a proportion to solve. Draw a vertical scale to make
sure we set up the correct proportion.
Solve: Estimate P/100 ≈ 50% for ≈1900 compared to ≈3800.
𝑃
1,890
Write the proportion.
=
100 3,740
3,740 ∙ 𝑃 = 189,000 Use cross products.
𝑃 = 189,000 ÷ 3,740 P is a missing factor, so divide.
𝑃 ≈ 50.5 Use a calculator and round.
50.5% is the percent P % is the percent.
Check: 50.5% fits our estimate of ≈ 50%, so we accept this answer.
ANSWER: Jeremiah’s current housing expenses are about 50.5% which is higher than
the 44% that the guidelines recommend. (Jeremiah has asked a good
question here, and now he has information to make some well-informed
decisions.)

Check Point 3
Colleen wants to keep her heart rate below 80% of her maximum heart rate of 180 beats per
minute. What is this heart rate?
403
404
SECTION 4.8 Solving Percents Using Proportions

Check Point 4
In 2012, a National Retail Foundation survey reported that the average “back to college”
expenses were $907.22 per college student with an average of $216.4 of this money spent on
computers and other electronics1. What is the percentage of these back-to-college expenses
are dollars that were spent on electronics?
In applications, percentages are often more than 100% or even less than 1%. For
instance, a nursing assistant (CNA) who earns a degree as a registered nurse (RN) will see his or
her wages grow more than 100% with the first pay check as an registered nurse. In 2011 the
205,000 people of Jackson County, Oregon, represented 0.066% of the population of the United
States. Learn to think through the mathematics when the percentages are not numbers that
we are used to seeing.
Example 5: Suzanne is thinking of taking a job in San Francisco. She earns $2,800 a month in
Eugene, Oregon, right now. Using a cost-of-living calculator that she found online2, Suzanne
discovered that she needs to earn $4,257 in San Francisco to have the same “purchasing
power” that she has in Eugene. What percentage of her current wage is the amount she would
need to earn to have the same purchasing power in San Francisco?
Think it through: Our answer will be more than 100% because $4,257 > $2,800.
Understand: Suzanne is looking for a missing percent.
Plan: Use a proportion to solve. Draw a vertical scale to make
sure we set up the correct proportion.
Solve: Using ≈ 4,500 𝑎𝑛𝑑 ≈ 3,000 for wages, estimate 𝑃 ≈
150 and our answer should be about150%.
1
http://www.nrf.com/modules.php?name=News&op=viewlive&sp_id=1405
2
http://cgi.money.cnn.com/tools/costofliving/costofliving.html
UNIT FOUR: Prealgebra in a Technical World
𝑃
4,257
= 2,800
100
2,800 ∙ 𝑃 = 425,700
Write a proportion.
Use cross products.
𝑃 = 425,700 ÷ 2,800 𝑃 is a missing factor, so divide.
𝑃 ≈ 152
152% is the percent.
Use a calculator.
𝑃% is the percent.
Check: Because the estimate and the computation agree, we accept this result.
ANSWER: According to the cost-of-living calculator we found online, Suzanne will
need to earn about 152% of what she now earns to enjoy the same
purchasing power in San Francisco as in Eugene.

Check Point 5
Many of today’s registered nurses worked as nursing assistants before going to school to
become RNs. While the average entry level salary for a nursing assistant in Oregon is $24,500,
the average entry level salary for a registered nurse in Oregon is $67,104 according to the
Oregon Employment Department3.
What percent of the average nursing assistant’s salary in Oregon is the average salary of
Oregon registered nurses?

Check Point 6
In 2012 the property tax rate for the Applegate District of Josephine County was $8.4390 dollars
per thousand dollars of assessed value. A house assessed at $120,000 would have been
charged a property tax of $1,012.68 in this tax district. What percent of $120,000 is $1,012.68?
3
http://www.qualityinfo.org/olmisj/OIC
405
406
SECTION 4.8 Solving Percents Using Proportions
Increases and Decreases with Percents
When wages go up by a certain percentage, the amount we are paid increases
proportionally. When the value of a house falls by a certain amount, we can find the
percentage that its value has decreased.
When these changes occur, we have more than one way to think about the percentages
and proportions involved. For instance Deirdre and Steve work for the same company, both
earn $10.80 per hour, and they find out that they are getting a 2.5% raise starting next month.
They both calculated their new salaries, but they each used different methods.
Deirdre’s Method
2.5
𝐴
=
100 10.80
𝐴 = $0.27
𝐴 = 10.80 + .27
𝑨 = $𝟏𝟏. 𝟎𝟕
Steve’s Method
Deirdre calculates the
amount of her increase
in wages.
100 + 2.5
She adds the new
amount to the original
base wage.
102.5
𝐴
=
100
10.80
Steve calculates the total
percentage for his new
wage.
= 102.5%
𝑨 = $𝟏𝟏. 𝟎𝟕
Steve finds the amount
using the percentage of his
original wage.
Both Deirdre and Steve need to know what their missing value is. In Deirdre’s case she solved a
proportion to find the amount of increase in her hourly wage. Steve solved a proportion to find
the new amount of his new wage.
FORMULA:
For problems with percent of increase:
 𝑨𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 = 𝑁𝑒𝑤 𝑇𝑜𝑡𝑎𝑙 𝑨𝑚𝑜𝑢𝑛𝑡 − 𝐵𝑎𝑠𝑒

𝑷𝑒𝑟𝑐𝑒𝑛𝑡 𝑜𝑓 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒
100
=
𝑨𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒
𝑩𝑎𝑠𝑒
(Deirdre’s method)
or…

100+ 𝑷𝑒𝑟𝑐𝑒𝑛𝑡 𝑜𝑓 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒
100
=
𝑁𝑒𝑤 𝑇𝑜𝑡𝑎𝑙 𝑨𝑚𝑜𝑢𝑛𝑡
𝑩𝑎𝑠𝑒
(Steve’s Method)
UNIT FOUR: Prealgebra in a Technical World
For problems with percent of decrease:

𝑨𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒 = 𝑩𝑎𝑠𝑒 − 𝑁𝑒𝑤 𝑇𝑜𝑡𝑎𝑙 𝑨𝑚𝑜𝑢𝑛𝑡

𝑷𝑒𝑟𝑐𝑒𝑛𝑡 𝑜𝑓 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒
100
=
𝑨𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒
𝑩𝑎𝑠𝑒
or…

100− 𝑷𝑒𝑟𝑐𝑒𝑛𝑡 𝑜𝑓 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒
100
=
𝑁𝑒𝑤 𝑇𝑜𝑡𝑎𝑙 𝑨𝑚𝑜𝑢𝑛𝑡
𝑩𝑎𝑠𝑒
Example 6: If a new car loses 25% of its value in one year, what is the decrease in value for a
$11,150 new car one year after it is purchased? What is the car worth after the first year?
Think it through: Find the amount of decrease first and then subtract from the base.
Understand: We are looking for the new total amount.
Plan: Find 25% of $11,150 and then subtract this from $11,150.
Solve: Because 25% is
Estimate:
1
4
1
4
, we can simplify this percentage problem.
of 12,000 is about a $3,000 depreciation, and so the car would
then be worth a bit less than $9,000 after the first year.
1
𝑨
Write a proportion, and simplify using
=
4 11,150
fractions.
4 ∙ 𝐴 = 11,150 Use cross multiplication.
𝐴 = 11,150 ÷ 4 𝐴 is a missing factor, so divide.
𝐴 = $2,787.50 Use a calculator.
11,500 - 𝐴 = 8,712.50 Subtract the depreciated amount.
Check: Because the depreciation, $2,787.50, is close to but less than $3,000,
and the difference is close enough to $9,000, we accept these answers.
ANSWER: One year after purchase the $11,150 new car has lost $2,787.50 in value.
The car is worth $8,362.50 after its first year.
407
408
SECTION 4.8 Solving Percents Using Proportions
When working with percentages of decrease, check closely to see if the question
asks for the amount of decrease or the amount left (what the car is worth now).
The last example asked both questions.

Check Point 7
The population of New Orleans was 455,100 people before Hurricane Katrina in August 2005.
In 2010, 343,829 people were living in New Orleans4. By what percentage had the population
decreased from the 2005 pre-Katrina levels?
Although many areas in the Mid-West are experiencing a population decrease, for most
Oregon counties the population is increasing.
Example 7: The population of Jackson County, Oregon, was estimated by the U.S. Census at
181,205 people for 2000. By the year 2010, the population5 had increased by 12%. What was
the population of Jackson County in the year 2010?
Think it through: This a percent of increase problem.
Understand: We are looking for the new total amount. We know the base
was 181,205. We know that we have added another 12% more people to
this base.
Plan: Find 12% of the base population and then add this to the base.
(Another plan would be to find 112% of the base population and be done.)
Solve: Estimate ≈200,000 by adding ≈ 10% more people.
4
http://www.infoplease.com/ipa/A0108219.html
5
http://quickfacts.census.gov/qfd/states/41/41029.html
UNIT FOUR: Prealgebra in a Technical World
12
𝑨
=
100 181,205
100 ∙ 𝐴 = 2,174,460
Write a proportion for the Amount of increase.
Use cross products and multiply.
𝐴 = 2,174,460 ÷ 100 𝐴 is a missing factor, so divide.
𝐴 = 21,744.6 Hopefully you divided using mental math!
181,205 + 21,744.6 ≈ 202,950
Add the base and the amount of increase.
Because these are people, round to the nearest
whole number.
Check: Using Steve’s method, we find 112% of 181,205. This is 202,950.
ANSWER: The population of Jackson County, Oregon, was about 202,950 in 2010.
 Check Point 8
Annika bought her home for $82,000 in 1990. Her home was recently appraised at $210,000.
What is percentage of increase in the house value? (In business this increase in the value of an
investment is called “appreciation.”)
Although we are not guaranteed that our houses will always appreciate, we do know
that most consumer goods decrease in value. (In business this decrease is called
"depreciation").
 Check Point 9
The first iPod held about 240 songs. It first became available in 2001 and sold for $499. Today
this model of the iPod sells new, in its original packaging, on auction Web sites for around $30.
What is the percent of decrease in the value of the original iPod?
409
410
SECTION 4.8 Solving Percents Using Proportions
UNIT FOUR: Prealgebra in a Technical World
4.8 Exercise Set
Name _______________________________
Skills
Write proportions to find the missing values.
(Round answers to the nearest hundredth place, or hundredth of a percent, when necessary.)
Percent
Amount
Base
Percent
Amount
Base
1.
30%
3.
75%
710
45
2.
215%
4.
0.40%
5.
71
163
6.
7.
3.9
19.86
8.
75
320
24
1.65%
2,221
12,544
Suppose your current wage is $533 per week. Find your new weekly salary if you are given the
following wage increases. (Use Deirdre's method, page 404.)
Percent Raise
9.
11.
New Weekly Salary
Percent Raise
2%
10.
3%
1.5%
12.
3.5%
New Weekly Salary
Suppose your current wage is $427 per week. Find your new weekly salary if you are given the
following wage increases. (Use Steve's method, page 404.)
Percent Raise
New Weekly Salary
Percent Raise
13.
1%
14.
3%
15.
1.5%
16.
2.2%
Applications
New Weekly Salary
UPS
Problems 17 to 20 require the following table.
Oregon State Income Tax Tables
Tax Rate Chart J: For persons filing "Jointly,"
Tax Rate Chart S: Persons Filing "Single" or
"Head of Household," or "Qualifying
"Married Filing Separately"
Widow(er) with Dependent Child”
Not over $3,050
5% of taxable income
Not over $6,010
5% of taxable income
Over $3,050 but not
$153 plus 7% of the
Over $6,010 but not
$305 plus 7% of the
over $7,600
excess over $3,050
over $15,200
excess over $6,010
$471 plus 9% of the
$942 plus 9% of the
Over $7,600
Over $15,200
excess over $7,600
excess over $15,200
411
412
SECTION 4.8 Solving Percents Using Proportions
(See table previous page.) Read the table to determine the expression you enter in your
calculator. Estimate and then use your calculator to answer. Problem 17 is done for you.
17. If a single person's taxable income is
$7,500, what is the tax amount?
18. If a single person's taxable income is
$34,750, what is the tax amount?
Calc. 𝟏𝟓𝟑 + 𝟎. 𝟎𝟕(𝟕, 𝟓𝟎𝟎 − 𝟑𝟎𝟓𝟎)
Calc. _____________________________
Ans.__$464.50
Ans.___________
19. If a couple files jointly with a taxable
income of $14,150, what is the tax
amount?
Calc. _____________________________
Ans.___________
20. If a head of household's taxable income
is $34,750, what is the tax amount?
Calc. _____________________________
Ans.___________
Federal income taxes must be calculated for the amount of income that falls into each bracket.
Complete problems 21 to 24 using the Federal tax table. Problem 21 has been completed for you.
2012 Federal Income Tax Brackets
Income
Married Filing Jointly
Married Filing
Tax
Single
or Qualified
Head of Household
Separately
Rate
Widow(er)
over
up to
over
up to
over
up to
over
up to
10%
$0
$8,700
$0
$17,400
$0
$8,700
$0
$12,400
15%
$8,700
$35,350 $17,400 $70,700
$8,700
$35,350 $12,400 $47,350
25%
$35,350 $85,650 $70,700 $142,700 $35,350 $71,350 $47,350 $122,300
28%
$85,650 $178,650 $142,700 $217,450 $71,350 $108,725 $122,300 $198,050
33%
$178,650 $388,350 $217,450 $388,350 $108,725 $194,175 $198,050 $388,350
35%
$388,350
$388,350
$194,175
$388,350
Use the above table for the following questions. The first one has been done for you.
21. If a single person's taxable income is
$57,500, what is the tax amount?
Calc. 0.25(57,500 − 35,350) +
10% of
8,700
22. If a single person's taxable income is
$34,750, what is the tax amount?
Calc. ____________________________
0.15(35,350 − 8,700) + 870__________
________________________________
Ans. $𝟏𝟎, 𝟒𝟎𝟓
Ans.___________
23. If a couple files jointly with a taxable
income of $14,150, what is the tax?
Calc. ____________________________
24. If a head of household's taxable income
is $34,750, what is the tax amount?
Calc. ____________________________
________________________________
________________________________
Ans.___________
Ans.___________
UNIT FOUR: Prealgebra in a Technical World
25.
A pair of $29.99 jeans is on sale for 20% off. You have a coupon for 25% off of the sale
price. If you use your coupon, how much will you pay for the jeans?
26.
Judy's monthly paycheck this month is $1,520.92. This reflects a cost-of-living raise of
3.5%. What was her monthly paycheck before the raise?
27.
Gregory bought a used car from a friend at the valuation set by Kelly Blue Book®. He paid
his friend $5,795, and his friend lamented that the car cost him $18,199 just 5 years ago!
What is the percent of decrease in value of Gregory's car over the last 5 years?
28.
Alvin's income tax went up $184 from last year. If his new tax bill is $905, what were his
taxes last year?
29.
Student loan debt in the US rose to $902 billion in 2012. This rose from $870 billion in the
third quarter of 2011. What is the percent of increase in student loan debt during this
time period?
30.
The original iPod weighed 6.5 oz. The iPod Touch® weighs 4.1 oz. By what percent did
the weight decrease in the iPod Touch®?
31.
With only one question wrong, your score is 95%. How many questions on the quiz?
32.
Felix got 190 correct out of 250 on his biology test. What percentage did he earn?
33. A family bought a house in 2005 for $242,500. They sold it in 2010 for $198,850. By what
percent did the house decrease in value?
413
414
SECTION 4.8 Solving Percents Using Proportions
34. You need to earn at least a 70% on the final in your math class. If the final is worth 150
points, what is the minimum number of points that you need to earn to get a 70%?
35. You have 300 points out of 450 points possible in your math class. Find:
a. What is your current percent in the class?
b. How many points must you earn on a 150 point final to have at least an overall
average of 70%?
36.
Penney's has a sale on t-shirts: buy two get two free. The t-shirts cost $20 a piece. You
also received a 15% off of any purchase coupon in the mail. If you buy 4 t-shirts:
a. What did you pay for 4 t-shirts if you used your 15% off coupon?
b. What was the average price of each t-shirt?
c. How much did you save on each t-shirt?
d. What percent did you save on each t-shirt?
Review and Extend
Calculate as many of the following as you can using mental math. Use paper and pencil for the
rest. DO NOT USE A CALCULATOR.
1 1
37. 2 + 3
4 1
38. − −
5 10
3
7
39. −3 + 4
8
8
5
2
5
−
(−4
)
40.
6
3
1
4
41. (− ) (− )
2
5
1
4
42. 3 (−1 )
3
5
5
3
2
÷
(−1
)
43.
8
4
44. (−2
1
1
) ÷ (−2 )
10
4
1
5
1
45. 3 − 1 − (− )
3
6
2