Free Pre-Algebra
Lesson 42 ! page 1
Lesson 42
A Few Consumer Percents
Some of the most common uses of percents involve money.
Sales Tax
Most governments raise their operating costs through taxes. One form of tax commonly imposed by state and local
governments in the U.S. is the sales tax. When an item is sold in a particular state, the state government collects a tax of
some percent of the sale price. (Sometimes there is an additional county, district, or city sales tax as well.)
When you buy an item, the price charged by the store is called the purchase price. Sales tax is added to the purchase price
at the time you buy the item. If you pick up an item that has a price tag reading $4.99, you will have to pay the $4.99 plus
some additional amount of sales tax at the register.
Table of Sales Tax Rates, by State (January, 2010)
Alabama
4.00%
Alaska
nil
Arizona
5.60%
Arkansas
6.00%
California
8.25%
Colorado
2.90%
Connecticut 6.00%
Delaware
nil
Florida
6.00%
Georgia
4.00%
Hawaii
4.00%
Idaho
6.00%
Illinois
6.25%
Indiana
7.00%
Iowa
6.00%
Kansas
5.30%
Kentucky
6.00%
Louisiana
4.00%
Maine
5.00%
Maryland
6.00%
Massachusetts 6.25%
Michigan
6.00%
Minnesota
6.88%
Mississippi
7.00%
Missouri
4.23%
Montana
nil
Nebraska
5.50%
Nevada
6.85%
New Hampshire nil
New Jersey
7.00%
New Mexico
5.00%
New York
4.00%
North Carolina
5.75%
North Dakota
5.00%
Ohio
5.50%
Oklahoma
4.50%
Oregon
nil
Pennsylvania
6.00%
Rhode Island
7.00%
South Carolina
South Dakota
Tennessee
Texas
Utah
Vermont
Virginia
West Virginia
Wisconsin
6.00%
4.00%
7.00%
6.25%
4.70%
6.00%
5.00%
6.00%
5.00%
Since the sales tax is a percent of the purchase price, the amount of tax you pay is proportional to the amount you spend.
You pay more tax on expensive items than on cheaper items.
The sales tax is a percent of the purchase price.
amount
=
percent
•
base
The amount of tax you pay is figured out as a part of the price, but then it is
added to the price. For example, if the tax is 6%, you figure out 6% of the
purchase price, then add it to the purchase price. The price you pay is 106%
of the purchase price.
+
For example, with a sales tax of 6%, an item with a purchase price $1.00 will
have a tax of $0.06 (6¢ is 6% of 100¢). This is why a 6% tax rate is sometimes
described as “six cents on the dollar.” You pay $1.00 + $0.06 = $1.06. $1.00 goes to the store, and the $0.06 goes to the
state government to pay for roads, schools, sewer lines, and other government services.
© 2010 Cheryl Wilcox
Free Pre-Algebra
Lesson 42 ! page 2
Example: On your visit to West Virginia, you found a great guitar that you want to buy. The store is charging
$1,250 for the guitar. What will the sales tax be? How much money do you need in all?
Sales tax in West Virginia is 6%, according to the table on the previous page. The base is the purchase price.
Sales tax = 6% of purchase price
Sales tax = 0.06 • $1250
Sales tax = $75
You have to pay the $1250 purchase price, plus $75 in sales tax, for a total of
$1250 + $75 = $1325
The total will be $1325.
Example: Now that you’re back home in California, you feel you must buy an amplifier that is priced at $550. How
much will you pay with tax included?
Sales tax in California is 8.25%, according to the table on the previous page. You can either figure out the sales tax, then
add it to the purchase price, OR you can find 108.25% of the purchase price. That’s 100% of the price, all of it, plus the
8.25% tax, all rolled up into one percent.
Price including tax = 108.25% of purchase price
Price including tax = 1.0825 • $550
Price including tax = $595.375
The price should be rounded to the nearest whole cent.
Price including tax = $595.38
Leaving a Tip
Eating in a restaurant in the U.S. usually involves leaving a tip for the wait staff. The standard amount for a restaurant tip is
15% to 20% of the cost of the meal. We’ll assume the cost of the meal is the price before any sales tax is added.
The tip
is a percent of the cost of the meal.
amount
=
percent
•
base
Like sales tax, a tip is figured out as part of the base price, but then it is added to the base price, becoming part of the total
+
cost of your meal.
The cost of the meal plus 15% tip.
+
The cost of the meal plus 20% tip.
+
© 2010 Cheryl Wilcox
+
Free Pre-Algebra
Lesson 42 ! page 3
Example: After enjoying their lovely anniversary dinner, Ashley and Clark must figure out the tip. The bill for the
dinner before tax was $78.00. They decide to leave a 20% tip because the service was so great. How much should
they leave?
The tip is 20% of the cost of the meal.
Tip = 0.2 • $78 = $15.60
20% of the cost of the meal is $15.60.
Because a tip is a variable percentage between 15% and 20%, Clark and Ashley might round down to $15, since that
amount will still be in the correct range.
Example: Like many restaurants, Jack’s includes a 15% gratuity (tip) on the bill for parties with 6 or more people.
The office lunch party at Jack’s had 8 people, and the bill came to $170. How much did the restaurant charge for the
gratuity?
The gratuity is 15% of the cost of the meal.
Gratuity = 0.15 • $170 = $25.50
15% of the cost of the meal is $25.50.
Since sales tax in California is 8.25%, if you double the sales tax you get 16.5%. Since 16.5% is between 15% and 20%,
many Californians figure out a restaurant tip by doubling the sales tax amount.
Example: Romelia had a salad and soft drink for a total of $11.99, and Hans had a burger and milkshake, which
cost $15.89. They decided to tip double the sales tax of 8.25%. How much did they pay, including sales tax and tip?
Romelia’s meal + Hans meal = combined cost of meal
$11.99 + $15.89 = $27.88
Sales tax is 8.25% of $27.88
Sales tax = 0.825 • $27.88 = $2.3001
The sales tax will be $2.30
The tip is twice the sales tax.
Tip is 2 • $2.30 = $4.60.
They pay $27.88 + $2.30 + $4.60 = $34.78
Interest on Loans or Savings
Another percent that is added to the base amount is the interest earned on savings or paid on a loan. Interest can be figured
in quite complicated ways, but the basic idea is to add some percent of the base (the money saved or borrowed) to the
base. Interest is like a fee charged for use of the money. If you keep your money in the bank, they use it and so pay you a
fee, which is some percent interest. If you borrow money from the bank, they charge you a fee for your use of the money,
again, some percent interest of the original loan.
Interest is a percent of the money saved or borrowed.
amount
=
percent
•
When doing interest calculations, the base is called the principal.
© 2010 Cheryl Wilcox
base (principal)
Free Pre-Algebra
Lesson 42 ! page 4
Example: At the beginning of the year, Harmony had $3,568.90 in her savings account, which earned 2% interest
each year. She didn’t spend any of the money. After one year had passed, the bank added the interest to the
account. How much interest did they add? How much money did Harmony have in the account after the interest
was added?
The interest is 2% of $3,568.90.
interest = 0.02 • $3,568.90
interest = $71.378
rounded to the nearest cent, $71.38
Harmony had $3,568.90 + $71.38 = $3,640.28
Example: Sahira borrowed $5,200 to buy a car, and agreed to pay back the loan amount plus 12% interest within
one year. How much did she pay back in all?
Like the sales tax, you can either figure out 12% interest and add it to the loan, or find 112% of the loan, which will be the
total amount to pay back.
total repayment is 112% of loan amount
= 1.12 • $5,200 = $5824
Sahira will end up paying back $5,824.
Sale Prices
The previous percents in this section were added on to the base. But a sale offers some percent off the original price, which
is subtracted from that price to make a new, cheaper price. When calculating percents in a sale, the base is always the
original price of the item.
The sale price is 15% off the original price.
The sale price is 40% off the original price.
The whole square is the original price.
The whole square is the original price.
The white squares represent the 15% taken off the price.
The 40% off is white.
The green squares that remain are the new sale price.
The new sale price is 100% – 40% = 60% of the original.
The green squares left represent the new sale price.
Notice that the green squares are
100% – 15% = 85% of the original price.
After subtracting 40%, you pay 60% of the original price.
There are two ways to find out how much you’re going to pay for an item on sale.
Method 1: You can figure out the savings and subtract that from the original price to find what you will pay.
Your savings are 40% of the original price.
Original price – savings = Price you pay.
© 2010 Cheryl Wilcox
Free Pre-Algebra
Lesson 42 ! page 5
Method 2: You can subtract the percent you save from 100% and use the result to calculate the price you pay.
Your savings are 40% of the original price.
100% – 40% = 60%
You pay 60% of the original price.
You should use whichever method makes the most sense to you, or the one that is easiest for the situation.
Example: That great leather jacket you’ve been wanting is finally on sale for 25% off. It originally cost $380. How
much will you save? How much will it cost?
You save 25% of $380.
You save 0.25 • $380 = $95.
100% – 25% = 75%
The cost is 75% of the original cost.
The cost is 0.75 • $380 = $285.
Note that $380 – $95 = $285.
!
© 2010 Cheryl Wilcox
Free Pre-Algebra
Lesson 42 ! page 6a
Lesson 42: A Few Consumer Percents
Worksheet
Name________________________________________
1. Suppose you go to Illinois and buy 2 tickets to see the
Bears in the playoffs. The tickets cost $450 each, and there
is also a $17.50 processing fee per ticket. The state sales
tax rate in Illinois is 6.25%, charged on the entire amount of
the sale, including fees. How much will the total be?
2. In California, cities and counties may impose additional
sales tax above the state tax. In Pleasant Hill, California, the
total state and local sales tax is 9.25%. Find the sales tax
you pay on a pair of shoes for $110 in Sun Valley mall in
Pleasant Hill, California.
3. The dinner bill was $85.60. Figure a tip of 15% and one of
20% on the bill.
4. Juaquin borrowed $3000 at 8% interest. At the end of the
year he must pay back the $3000 plus the interest. How
much will he pay in all?
5. Shayla saved 25% on the bedlinens. The original price
was $145. How much did she save? How much did she
pay?
6. The jeans originally cost $85, but the sale was for 40%
off. What was the sale price of the jeans?
7. “See this nifty hedgetrimmer? What a great sale! 60% off!
I saved $54.”
8. Lindsey found the same Baby PlayZone that sells for
$119.99 at the store for $20 at a garage sale.
“How much was it originally?”
The garage sale price is what percent of the store price?
“How much did you spend?”
What percent did Lindsey save?
© 2010 Cheryl Wilcox
Free Pre-Algebra
Lesson 42 ! page 7
Lesson 42: A Few Consumer Percents
Homework 42A
1. You are making a large sign to advertise the big prize in
your club’s raffle – an iPod shuffle. The shuffle is 1.24 inches
wide and 1.14 inches tall. If your picture will be 16 inches
wide, how tall should it be to be similar to the real shuffle?
Name________________________________________
2. Revell 1:39 Wright Flyer "First Powered Flight"
1:39 Scale. Measures 6 3/4" in length and has a wingspan
12 1/4". December 17, 1903: Orville and Wilbur Wright made
history one century ago on the sands of Kitty Hawk, NC, when they
successfully flew the flying machine that they had built.
What was the length and
wingspan of the original Wright
Brother’s flying machine, in feet?
3.Gasoline weighs 6.073 pounds per gallon. If you fill your
gas tank with 30 gallons, how much does the gas weigh?
4. The average height of a man in the U.S. in 2010 was
5’10”. The average weight was 191 lbs. Find the average
BMI for men in the U.S. based on the average height and
weight.
BMI =
703W lb
(H in)2
5. If you travel 336 miles on your 30 gallons of gas, what is
your gas mileage?
6. A house that costs $488,750 is 1,850 square feet. What is
the price per square foot?
7. Fill in the table with the missing equivalents.
8. Fill in the table with the missing equivalents.
FRACTION DECIMAL PERCENT
FRACTION DECIMAL PERCENT
1/8
1%
1/4
2%
3/8
6.25%
1/2
9.75%
7/8
11.2%
© 2010 Cheryl Wilcox
Free Pre-Algebra
Lesson 42 ! page 8
9. Leisha’s home is 1,625 square feet and she is using 450
square feet for her daycare business. To figure out her tax
deduction she has to find the percent of her home’s square
footage used by her business.
10. Shasha found that there were 1,483 songs on his iPod
that he had only listened to once. His iPod held 9,447 songs.
What percent of the songs had he listened to only once?
11. A ballot measure passed with 63% of the vote. If
276,801 people voted, how many voted in favor?
12. Drew Brees completed 68.1% of the 658 passes he
attempted in 2010. How many passes did he complete?
13. You are buying a new car for $28,799. You can buy it in
Sacramento, where the sales tax rate is 8.75% or in Walnut
Creek, where the sales tax rate is 9.25%. How much will you
save on sales tax if you buy the car in Sacramento?
14. Brittney was visiting her cousins in another state and
thought the sales tax seemed low. She had bought a
souvenir for $19.99 and the sales tax was $0.80. What was
the sales tax rate?
15. The waiter was so funny and sweet that we decided to
leave him a 20% tip. The meal cost $72.80. What was the
tip?
16. The savings of $5230 will earn 1.8% interest this year.
How much will the interest be?
17. A new copy of the textbook costs $162.67. If a used
copy is 60% off the price of a new copy, what is the used
textbook price?
18. For a limited time, you can save 30% on a gym
membership. The usual price is $35 per month. What is the
discounted price?
© 2010 Cheryl Wilcox
Free Pre-Algebra
Lesson 42 ! page 9
Lesson 42: A Few Consumer Percents
Homework 42A Answers
1. You are making a large sign to advertise the big prize in
your club’s raffle – an iPod shuffle. The shuffle is 1.24 inches
wide and 1.14 inches tall. If your picture will be 16 inches
wide, how tall should it be to be similar to the real shuffle?
W
1.24 16
=
H
1.14 h
1.24h = 16 • 1.14
1.24h = 18.24
1.24h / 1.24 = 18.24 / 1.24
h ! 14.7
2. Revell 1:39 Wright Flyer "First Powered Flight"
1:39 Scale. Measures 6 3/4" in length and has a wingspan
12 1/4". December 17, 1903: Orville and Wilbur Wright made
history one century ago on the sands of Kitty Hawk, NC, when they
successfully flew the flying machine that they had built.
What was the length and
wingspan of the original Wright
Brother’s flying machine, in feet?
length:
263.25 / 12 = 21.9375 feet
wingspan:
6.073 lb
x lb
=
1 gallon 30 gallons
It weighs 182.19 lbs.
5. If you travel 336 miles on your 30 gallons of gas, what is
your gas mileage?
336 miles
30 gallons
= 11.2 miles per gallon
7. Fill in the table with the missing equivalents.
FRACTION DECIMAL PERCENT
1 12.25
=
W = 477.75 inches
39
W
477.75 / 12 = 39.8125 feet
The picture should be 14.7 inches high.
3.Gasoline weighs 6.073 pounds per gallon. If you fill your
gas tank with 30 gallons, how much does the gas weigh?
1 6.75
=
L = 263.25 inches
39
L
4. The average height of a man in the U.S. in 2010 was
5’10”. The average weight was 191 lbs. Find the average
BMI for men in the U.S. based on the average height and
weight.
BMI =
703W lb
703(191)
702
2
(H in)
= 27.4
6. A house that costs $488,750 is 1,850 square feet. What is
the price per square foot?
$488,750
1,850 sq ft
= $270.78 per square foot
8. Fill in the table with the missing equivalents.
FRACTION DECIMAL PERCENT
1/8
0.125
12.5%
1/100
0.01
1%
1/4
0.25
25%
1/50
0.02
2%
3/8
0.375
37.5%
1/16
0.0625
6.25%
1/2
0.5
50%
39/400
0.0975
9.75%
7/8
0.875
87.5%
14/125
0.112
11.2%
© 2010 Cheryl Wilcox
Free Pre-Algebra
Lesson 42 ! page 10
9. Leisha’s home is 1,625 square feet and she is using 450
square feet for her daycare business. To figure out her tax
deduction she has to find the percent of her home’s square
footage used by her business.
450 ft 2
1625 ft 2
= 0.2769... ! 28%
28% of her home is used by her business.
11. A ballot measure passed with 63% of the vote. If
276,801 people voted, how many voted in favor?
10. Shasha found that there were 1,483 songs on his iPod
that he had only listened to once. His iPod held 9,447 songs.
What percent of the songs had he listened to only once?
1483 songs
= 0.15698... ! 16%
9447 songs
About 16% of his songs.
12. Drew Brees completed 68.1% of the 658 passes he
attempted in 2010. How many passes did he complete?
0.63 • 276,801 = 174,384.63
0.681 • 658 = 448.098
About 174,385 people voted in favor.
He completed 448 passes.
13. You are buying a new car for $28,799. You can buy it in
Sacramento, where the sales tax rate is 8.75% or in Walnut
Creek, where the sales tax rate is 9.25%. How much will you
save on sales tax if you buy the car in Sacramento?
14. Brittney was visiting her cousins in another state and
thought the sales tax seemed low. She had bought a
souvenir for $19.99 and the sales tax was $0.80. What was
the sales tax rate?
Sacramento: 0.0875 • $28,799 = $2,519.91
percent • 19.99 = 0.8
Walnut Creek: 0.925 • $28,799 = $2,663.91
0.8 / 19.99 = 0.04002001
You save $144 by buying in Sacramento.
The sales tax rate is 4%.
15. The waiter was so funny and sweet that we decided to
leave him a 20% tip. The meal cost $72.80. What was the
tip?
0.2 • $72.80 = $14.56
The tip is about $14.50.
17. A new copy of the textbook costs $162.67. If a used
copy is 60% off the price of a new copy, what is the used
textbook price?
16. The savings of $5230 will earn 1.8% interest this year.
How much will the interest be?
0.018 • $5230 = $94.14
The interest is $94.14.
18. For a limited time, you can save 30% on a gym
membership. The usual price is $35 per month. What is the
discounted price?
100% – 60% = 40%
100% – 30% = 70%
0.4 • $162.67 = $65.068
0.7 • $35 = $24.50
rounded to the nearest cent, $65.07.
The discounted price is $24.50
The used book costs $65.07.
© 2010 Cheryl Wilcox
Free Pre-Algebra
Lesson 42 ! page 11
Lesson 42: A Few Consumer Percents
Homework 42B
Name_________________________________________
1. An iPad is 9.56 inches high by 7.47 inches wide. The
giant cardboard display iPad is 5 feet wide. How high is it?
2. 1/650 Eiffel Tower Heller Plastic Model
Scale: 1/650; Width: 7-1/2"; Height: 19"
Find the width and height of the real Eiffel
Tower in feet.
3.Gasoline weighs 6.073 pounds per gallon. If you fill your
gas tank with 20 gallons, how much does the gas weigh?
4. The average height of a woman in the U.S. in 2010 was
5’4”. The average weight was 164 lbs. Find the average BMI
for women in the U.S. based on the average height and
weight.
BMI =
703W lb
(H in)2
5. If you travel 316 miles on your 20 gallons of gas, what is
your gas mileage?
6. A house that costs $366,250 is 1,550 square feet. What is
the price per square foot?
7. Fill in the table with the missing equivalents.
8. Fill in the table with the missing equivalents.
FRACTION DECIMAL PERCENT
FRACTION DECIMAL PERCENT
1/10
15%
1/5
21%
7/10
102%
91/100
8%
1/50
0.5%
© 2010 Cheryl Wilcox
Free Pre-Algebra
Lesson 42 ! page 12
9. Sandra’s home is 1,975 square feet and she is using 780
square feet for her daycare business. To figure out her tax
deduction she has to find the percent of her home’s square
footage used by her business.
10. Julianne has 6,455 songs on her iPod, and 2,321 songs
have been played over 20 times each. What percent of the
songs have been played more than 20 times?
11. A ballot measure failed because only 37% of voters were
in favor. If 276,801 people voted, how many voted in favor?
12. Drew Brees completed 70.6% of the 514 passes he
attempted in 2009. How many passes did he complete?
13. You are buying a new car for $35,899. You can buy it in
Sacramento, where the sales tax rate is 8.75% or in Walnut
Creek, where the sales tax rate is 9.25%. How much will you
save on sales tax if you buy the car in Sacramento?
14. Alisha was excited to visit Paris, but shocked to discover
that the VAT (value added tax, like U.S. sales tax) was
19.6%. If she spent 85 Euros at a shop, what was the VAT
on her purchase? How much did it cost in all?
15. The service was not very good, so we left a smaller tip,
only $15.00 even though our meal cost $118.80. What
percent did we tip?
16. The savings of $2,885 will earn 1.68% interest this year.
How much will the interest be?
17. A new copy of the textbook costs $109.76. If a used
copy is 45% of the new price, what is the used textbook
price?
18. For a limited time, you can save 40% on a gym
membership. The usual price is $42 per month. What is the
discounted price?
© 2010 Cheryl Wilcox