Transcript Tips, Discounts, Tax - Mrs. Graf's Seventh Grade Mathematics

Learning Target:
I can…
Use a proportion to find percent increase and
decrease
Percent Increase and Decrease
Percent Increase: when the value exceeds
100% of the original value
Percent Decrease: when the value is less
than 100% of the original value
To Find a New Value
1) Use a ____________________ to solve percent
increase and decrease problems.
2) The increase or decrease gets ________ or
________ to/from 100. In the proportion, this
number goes over _________.
3) The original value should match up with 100.
Example 1
The Waynesville High School library has 500
books. Next year, they would like to increase
the number of books they have by 52%. If they
reach their goal, how many books would they
have next year?
Example 2
The Waynesville High School band has 45
members. Next year, they would like to increase
their membership by 20%. If they reach their
goal, how many members would they have next
year?
Example 3
The Dayton Transportation Department
recorded 200 crashes in October. Next month,
they would like to decrease their crashes by
25%. If they reach their goal, how many crashes
would they have next month?
Example 4
The Dayton Fire Department recorded 120 fires
in October. Next month, they would like to
decrease the fires by 20%. If they reach their
goal, how many fires would they have next
month?
To find a percent increase or decrease:
Example 1: Janie starts playing sports and gets
into shape. She goes from 125 pounds to 110
pounds. Is this a percent increase or decrease?
What was her percentage weight loss?
*Remember: the original value always matches
up with 100
2)
Growing up, you lived in a tiny country village.
When you left for college, the population was
840. You recently heard that the population
was 882. Is this a percent increase or
decrease? What is the percent change?
3)
One week 24 people in Waynesville got
speeding tickets. The next week only 16 people
got speeding tickets. Is this a percent increase
or decrease? What is the percent change?
4)
Last year, only 8 athletes played on the girls
tennis team. This year 10 people played. Is this
a percent increase or decrease? By what
percentage?
Mix it up
A girl was 4 ft 9 in. tall last year. This year she is
5 ft tall. Find the percent of increase in her
height. Round to the nearest tenth of a
percent.
A. 2.0%
B. 5.3%
C. 5.0%
D. 153.0%
When the first US Census was taken in 1790,
the population was 3,929,200. In the most
recent census, the population was
308,745,538. What is the percent increase
rounded to the nearest tenth?
Last year 300 kids went to Waynesville Middle
School. This year, 350 kids go to Waynesville
Middle School. What is the percent of
change?
In the 1986 Olympic Games, Ellery Clark of the US
jumped 20 ft 10 in to win the men’s long jump.
In a recent Olympics, an athete jumped 28 ft 0.75
inches to win the men’s long jump. Find the
percent of increase or decrease in the length of
the men’s winning long jump.
OAA Practice:
What has the greatest percent of change?
A. A tree grew from 6 feet to 12 feet
B. An aquarium that was originally priced at $80
is now $60
C. A person whose salary was $100 per week is
now earning $120 per week
D. A baby who weighed 7 pounds at birth now
weighs 16 pounds
EXIT
Learning Target:
I can…
Calculate tax, gratuity and total bill
Percent Vocabulary
Gratuity:
Wholesale price:
Retail Price:
Markup:
Markdown:
Commission:
Interest:
Vocabulary
Gratuity:
(Tip) A percent earned by a person for
providing a service
Tax
The tip is a ___________________ of your bill
Step 1: ____________________ the percent
by the bill to get the tip
Step 2: ___________ the answer to
____________________________
Tips
You want to leave a 15% tip. If your meal costs
$10, how much should you leave for a tip?
How much did you spend altogether?
Step 1: Multiply (to get your tip)
Step 2: Add tip to the original amount to get the
total!
Example 2:
You want to leave a 20% tip. If your meal costs
$15, how much should you leave for a tip?
How much did you spend altogether?
Example 3:
If they only ask for your final payment:
You want to leave a 15% tip. If your meal cost
$30, how much did you spend altogether?
Tips
Example 4:
Your bill at Bob Evans is $25.00. If you
want to leave 20% gratuity, what will be the
total amount that you spent?
$25.00
Your parents took your family out to dinner.
Your parents wanted to give the waiter a 15%
tip. If the total amount of the dinner was $42,
how much should be paid to the waiter as a
tip?
How much will you spend all together?
Going Backwards: Example 1
Justin leaves a tip of $6, which was 20% of the
cost of his meal. How much did his meal cost?
Example 2
Eric’s family leaves a tip of $18, which was 15%
of the cost of their bill. How much did their
meal cost?
Vocab:
Sales Tax: A percent of a purchase charged by
the government
Tax is a ___________________ OF your
purchase
Step1: ____________________ the percent by
the purchase to get the tax
Step 2: ___________ the answer to
____________________________
Sales Tax
The sales tax is 6.5%. If you buy a television for
$500, what will your total price be?
Step 1: Multiply the percent by your price (to get
your tax)
6.5% x 500 = 32.5 or 32.50
Step 2: Add tax to the original amount to get the
total!
500 + 32.50 = $532.50 Total Price
You try it!
The sales tax is 7%. If you spent $60 on items,
how much is your sales tax?
$4.20
Including tax, how much did you spend?
$64.20
Example 3
Menu:
• Hamburger meal $8.75
• Drink $2.50
You and your friend each order a hamburger meal
and a drink. What is your total amount you will
spend?
What is the tax of the meal with a 6.5% tax?
What is the final bill?
Example 4
Example 4:
The bill for a family dinner was $49.53.
What is the bill with a 6.5% tax?
What is the total so far?
Mr. Jones wants to leave about 15% of the bill as a
tip. What is the tip?
What is the total amount he paid?
Exit
1. Find total amount spent at Best Buy if you
bought a $200 TV and paid 7% tax.
2. Find the total amount spent at a restaurant if
the bill is $30 and you tip 20%.
Learning Target:
I can…
Calculate markdowns
Markdown:
(Discount): A percent or amount of decrease in the price of an
item
Wholesale price:
The price a retail store pays the manufacturer
Markup:
A percent or amount increase a retail store charges to earn a
profit
Retail price: The price at which a store sells items to customers
(wholesale price + markup)
To calculate discounts and/or multiple discounts:
Step1: ____________________ the percent by the
purchase
Step 2: ___________ the answer from
____________________________
(Sometimes) Step 3: _____________ the additional
percentage by the new sale price
(Sometimes) Step 4: _____________ the additional
discount by the new sale price
1. Find 30% off of a CD that cost $15.
2. A stereo is $56.80. It is marked as 15% off
the original price. What is sale price?
3. A sweater is selling at a discount of 45%. The
original price is 49.60. What was the sale price
of the sweater?
The sweater shack is offering a 20% discount on
sweaters. If the regular price of the sweater is
$15.00, what is the discount?
Subtract the discount you found from the
original price to find the sale price.
Jean Junction is selling jeans at 25% off. The
regular price of the jeans are $40. What is the
discount?
What is the sale price?
A video game store has a 20% discount on all
video games. The video game you want is
$32. What is the discount?
What is the sale price?
Dacor Appliances is selling its $450 washing
machine for 15% off the regular price. What is
the discount?
What is the sale price?
You try it!
The original price of a DVD is $20.00. If it is
discounted 15%, what is the new price of the
DVD?
17
4. Elise is buying two coats for her children.
Margaret’s coat costs $40.00 but is 25% off.
Justin’s coat cost $34.00 but is 10% off. Which
coat is the better deal?
• If she buys them both, how much will she
spend? (without tax)
Discounts and Tax
1) A pair of jeans that you want to buy costs $24.00.
The jeans are on sale for 15% off. Sales tax is 7% added
to the price. What will the total be at the checkout?
– What is the discounted price? _________
– What is 7% of the discounted price _______
– What is your final total at checkout ________
2) Aimee is decorating her new house. She
found a table at Pier One for $425. If the table is
25% off and she has to pay a 6% tax, what will
be her final price at checkout?
• What is the discounted price? ________
• What is 6% of the discounted price? ______
• What is your final total at checkout?
___________
Multiple Discounts
1)
2)
3) Extended Response Example
Going Backwards (to find the original
price)
It may be helpful to set up a
___________________________.
Example 1:
A TV is selling at a discount of 25%. The sale
price is $609.75. What was the original price of
the TV?
Example 2:
A shirt is selling at a discount of 10%. The sale
price is $27.00. What was the original price of
the TV?
EXIT
The new price of a pair of pants is $30.00. find
the original price if the pants are discounted
20%.
EXIT
The original price of a pair of pants is $30.00.
find the new price if the pants are discounted
20%.
Learning Target:
I can…
Solve multi-step word problems involving
percent
Review – Gratuity
Step 1: __________________ the percent by the
bill to get your tip.
Step 2: _____________ your answer to the
original bill
Review – Gratuity
1. Janet got lunch at Deb’s Diner. She spent
$2.25 on a drink, $7.99 on a sandwich, and
$3.76 on dessert. She also left a 20% tip. How
much did she spend altogether?
Markdown
Step 1: __________________ the percent by the
purchase to get the discount
Step 2: _____________ your answer from the
original bill
Review - Discount
The sweater shack is offering a 15%
discount on sweaters. If the regular
price of the sweater is $18.00, what is
the new price of the sweater?
Multiple Discounts
Step 1: _____________ the percent by the cost
Step 2: _____________ the discount from the cost
Step 3: _____________ the addition percentage by
the new cost
Step 4: _____________ the discount from the cost
1) Stacy went to the shopping mall. While she
was shopping, she found a coat she liked that
was on sale. The coat originally cost $120 but
had been reduced by 35%. The store was having
a red tag sale that day, so she got an addition
10% off the sale price. How much did Stacy pay
for the coat?
A. $42.50
B. $66.00
C. $70.20
D. $78.00
2) The original price of a GPS system was
$105. It was on sale at a 20% discount. Later,
the price of the GPS was reduced by an
additional 10%. What was the final price of
the system?
Tax and Discount
Step 1: _______________ the percent by the
purchase to get the discount.
Step 2: ____________ your answer from the
original bill
Step 3: _____________ the percent tax by the new
bill to get the tax
Step 4: __________ the tax to your bill
Tax and Discounts
Andrea works as a cashier in a music store. A customer wants to
pay for a CD that is on sale for 15% off the regular price of
$14.00.
Andrea needs to add 7% sales tax
to the sale price of the CD. What
should Andrea charge the
customer for the CD, including
tax?
Clicker Check
A pair of jeans that you want to buy costs
$40.00. The jeans are on sale for 20% off. Sales
tax is 7% added to the price. What will the
total be at the checkout?
Working Backwards
A TV is selling at a discount of 20%. The
sale price is $799.20. What was the
original price of the TV?
The price of purchase was $53 after tax. If the
tax was 6%, what was the cost before tax.
EXIT
Ronny wants a pair of jeans that cost $40. The
jeans are on a markdown rack of 20% off. Ronny
has a coupon that says “take an additional 10%
off clearance items.” What is the final cost of
the jeans (without tax)?
RED, YELLOW, GREEN
6 – 7 correct, GET THE RED PAPER
3 – 5 correct, GET THE YELLOW PAPER
0 – 2 correct, GET THE GREEN PAPER
GREEN
*ALL OGT Questions*
1)
2)
3) Kelsey bought flowers from a florist for her
mom’s birthday. Kelsey bought a dozen
roses and was charged $20.25. If tax was
6%, how much did each rose cost before
tax?
Name__________________________
4) A local art museum charges admission to
groups according to the following rates.
Groups of fewer than 50 people are charged
a rate of $4.00/person. Groups of 50 people
or more are charged a reduced rate of
12.5% off per person. How much money will
a group of 49 people save in admission costs
if it can recruit one additional member?
5)
6)
YELLOW
Name__________________________
OGT Question
COUPON
1 pair of shorts regular priced
+1 pair half off
Equals
1)
______
______
______
SALE
30% off the first pair of shorts _____
+30% off the second pair
______
Equals
_______
Conclusion:
OAA Question
2) During a sale, the price of all televisions
in a store is being reduced by 30%. Sam
is interested in a television with an
original cost of $650.
Two weeks later, the same price of this
television is reduced by an additional
10%. Sam thinks he can now get the
television for 40% off the original price.
Describe how the same price with an
additional 10% reduction is different
than a single reduction of 40%. Use
mathematics to justify your answer.
30% with addition 10%
30% discount ______
Subtract to find sale price ______
10% of THAT SALE PRICE
______
Subtract to find final price _______
40%
40% discount _____
Subtract to find sale price______
Conclusion (are the answers the same, or how are they different?):
3) Joe wants to buy a shirt that is
regularly $20.00, but today it is on
sale for 40% off. When he gets to
the register, he remembers that
he will have to pay 6.5% sales tax
on the shirt as well. What is his
total?
DISCOUNT
Take 40% of 20 ______
Subtract this answer from 20______
TAX
Take your FINAL ANSWER from discount and multiply it by
6.5%_____
Add this answer to your FINAL ANSWER from discount______
FINAL ANSWER:
4)
*no hints*
Name__________________________
RED
*Questions with hints*
2) Jean Junction is selling jeans at 25% off. The regular price of
1) A shirt costs $35. There is a 16%
discount. What is the discount?
TO SOLVE: Multiply 16% by 35
the jeans are $40. What is the discount?
TO SOLVE: Multiply 25% by 40
How much do you pay for the shirt?
TO SOLVE: Subtract 35 by the discount
that you just calculated
What is the sale price?
TO SOLVE: Subtract 35 by the discount that you just
calculated
*Questions without hints*
3) The sweater shack is offering a 20%
discount on sweaters. If the regular
price of the sweater is $15.00, what is
the discount?
What is the new price?
4)
A video game store has a 20%
discount on all video games. The
video game you want is $32. What
is the discount?
What is the sale price?
*OAA Questions with hints*
5)
Step 1: Take 25% of 40 ______
Step 2: Subtract your answer from 40 ______
Step 3: Take 10% of step 2’s answer ______
Step 4: Subtract step 3’s answer from the step 2’s answer ______
*OAA Question without hints*
6)
You Try!
Daniel bought a pair of
pants that were on sale for
30% off, plus an additional
10% off the marked down
price. The original price of
the pants was $50.
What was the final price of
the pants?
Step 1: Take 30% of 50 ______
Step 2: Subtract your answer from 50 ______
Step 3: Take 10% of step 2’s answer ______
Step 4: Subtract step 3’s answer from the step 2’s
answer ______
July 5: Take 20% of 3,900 _____
Subtract your answer from 3,900 ______
July 6: Take 20% of July 5’s answer ______
Subtract this from July 5’s answer _______
Continue until your answer is under $2,200
CPS Mini Quiz
1. The sweater shack is
offering a 15% discount on
sweaters. If the regular price
of the sweater is $18.00,
what is the new price of the
sweater?
Name__________________________
2. Janet got lunch at Deb’s
Diner. She spent $2.25 on a
drink, $7.99 on a sandwich,
and $3.76 on dessert. She also
left a 20% tip. How much did
she spend altogether?
3. The original price of a GPS
system was $105. It was on
sale at a 20% discount. Later,
the price of the GPS was
reduced by an additional
10%. What was the final price
of the system?
4. A pair of jeans that you
want to buy costs $40.00. The
jeans are on sale for 20% off.
Sales tax is 7% added to the
price. What will the total be
at the checkout?
5. A TV is selling at a discount of 20%.
The sale price is $799.20. What was the
original price of the TV?
Learning Target:
I can…
Solve real-life word problems involving percent
Exit
You are buying 2 sets of pajamas. Which store
has the better buy and how much would you
spend?
Babies R Us
Buy 1 pair and
get one half off.
Original price:
$20.00
Target
Each pair is 30% off.
Original price:
$20.00
Learning Target:
I can…
Find the better buy
EXIT
Sarah’s Shoes is having a deal where
you can buy one pair of shoes and get
another half off. The shoes cost $40
per pair.
Steve’s Sneakers has a special where
you can get 20% off each pair you
buy. The shoes originally cost $35 per
pair.
If you want to buy 2 pairs, which store
has the better deal and how much will
you spend?
Learning Target:
I can…
Solve word problems involving interest
Simple Interest
• A percentage of a principal amount
Formula:
I=PxRxT
Where I is ___________________
P is _________________ or ____________
R is ___________
T is ___________
1) Suppose a bank is offering its customers 3%
interest on savings accounts. If a customer
deposits $1500 in the account, how much
interest does the customer earn in 5 years?
How much does the customer have in the bank
after 5 years?
2) Kelly plans to put her graduation money into an
account and leave it there for 4 years while she goes
to college. She receives $750 in graduation money
that she puts it into an account that earns 4.25%
interest. After 4 years, how much has Kelly earned
in interest?
How much will be in Kelly’s account at the end of
four years?
3) Suppose you put $200 in an account that pays
simple interest. The bank will pay you 5%
interest annually. How much interest will you
earn in three years?
How much total will you have in your account
after three years?
4) Adam plans to put his birthday money into
an account and leave it there for 10 years. He
receives $400 in birthday money that he puts
into an account that earns 5% interest. After 10
years, how much has Adam earned in interest?
How much will be in Adam’s account at the end
of ten years?
Working Backwards
I = $200
P = $1000 t = 5 years
Find the interest rate.
Working Backwards
I = $9
P = $200 t = 18 months
Find the interest rate.
You put $300 in a savings account. The account
earns $6 simple interest in 6 months. What is
the annual interest rate?
Finding the time
Find the amount of time
I = $30, P = $500, r = 2%
Finding the time
Find the amount of time
I = $144, P = $600, r = 4%
Vocab
Commission:
A percent of total sales earned by an employee
or business
Donald is a car salesman. Donald makes 10%
commission on every car he sells. If he sells a
car for $30,000, how much money does Donald
make?
Leo is a sells suits. He earns 30% commission for
each suit he sells. If he sells 5 suits and they
each cost $200, how much did he earn in
commission?
Tara is a sales representative for a cosmetic
company. She is paid $5.15 per hour each week
plus a commission of 10% of the amount of
sales over $5000. She works 40 hours one week,
and she sells $7260 worth of cosmetics during
that week. How much commission does she
make?
How much money does she make total?
Ryan is a sales representative for an insurance
company. He is paid $10 per hour each week
plus a commission of 5% of the amount of sales
(of insurance plans) over $2,000. He works 40
hours one week, and he sells $5,000 worth of
insurance during that week. How much
commission does she make?
How much money does he make total that
week?
Exit
Find the interest if Ayanna invested $5000 for 5
years at a rate of 3.5%. How much does she have in
the bank now?
Homework – page 140
Learning Target:
I can…
Solve word problems involving markup
Wholesale price:
The price a retail store pays the manufacturer
Markup:
A percent or amount increase a retail store
charges to earn a profit
Retail price: The price at which a store sells
items to customers (wholesale price + markup)
To Find the Retail Price:
Step 1: ______________ the wholesale price by
the markup rate
Step 2: ____________ the answer to the
wholesale price to get the retail price
1) A computer software retailer used a markup
rate of 40%. Find the selling price of a computer
game that cost the retailer $25.
2) A store that sells skateboards buys them
from a manufacturer at a wholesale price of
$57. The store’s markup is 150%. What is the
retail price?
3) A store buys guitars from a manufacturer at a
wholesale price of $38. The store’s markup is
85%. What is the retail price?
4)
Critical Thinking
A $140 car stereo is marked up 50% and then
discounted 50%. Will the final price of the car
stereo be $140? Explain.
To find the wholesale price
Use a proportion:
Step 1: __________________ the markup
percentage to 100%
Step 2: Put the new percentage over
_________________
Step 3: Always match up the wholesale price (x)
with 100
1) A shoe store uses a 40% markup on cost. Find
the wholesale price of a pair of shoes that sells
for $63.
Find the wholesale price
2) A bathing suit store uses an 80% markup on
cost. Find the wholesale price of a bathing suit
that sells for $40.
Find the rate of markup
To Find the Markup Rate
Step 1: Write a ratio of retail to wholesale
Step 2: Put the percentage (x) over____________
Step 3: Always match up the wholesale price (x)
with _______________
Step 4: _______________________the answer
from 100
Find the rate of markup
1) A golf shop pays its wholesaler $40 for a
certain club, and then sells it to a golfer for $75.
What is the markup rate?
Find the rate of markup
2) A tennis shop pays its wholesaler $20 for a
certain racket, and then sells it to a tennis player
for $50. What is the markup rate?
Profit
3) A store buys an item for $20. To earn a profit
of $30, what percent does the store need to
markup the item?
Profit
4) A store buys an item for $10. To earn a profit
of $20, what percent does the store need to
markup the item?
EXIT
Target buys a box of cereal for $1.50. If they
mark up the cereal 80%, what price do they sell
if for?
Homework – Page 136 in Record and Practice
Journal
Percent Error
Learning Target:
I can…
Review for my ratio, proportion and percent test
Vocab
Commission:
A percent of total sales earned by an employee
or business
Donald is a car salesman. Donald makes 10%
commission on every car he sells. If he sells a
car for $30,000, how much money does Donald
make?
Leo is a sells suits. He earns 30% commission for
each suit he sells. If he sells 5 suits and they
each cost $200, how much did he earn in
commission?
Tara is a sales representative for a cosmetic
company. She is paid $5.15 per hour each week
plus a commission of 10% of the amount of
sales over $5000. She works 40 hours one week,
and she sells $7260 worth of cosmetics during
that week. How much commission does she
make?
How much money does she make total?
Ryan is a sales representative for an insurance
company. He is paid $10 per hour each week
plus a commission of 5% of the amount of sales
(of insurance plans) over $2,000. He works 40
hours one week, and he sells $5,000 worth of
insurance during that week. How much
commission does she make?
How much money does he make total that
week?
EXIT
Proportion Review:
Matty was boiling a pot of water on the stove.
The temperature rose from 52°F to 92°F in 30
seconds. How many minutes would it take for
the temperature to boil (rise from 52°F to
212°F)?
Learning Target:
I can…
Show what I know on my ratio, proportion and
percent test
EXIT
Suppose that a ladybug can fly 70 feet in 5
seconds. A bee can fly 102 feet in 6 seconds.
Which can fly faster and by how much?
Learning Target:
I can…
Explain my misconceptions and correct my
mistakes
EXIT
Carla rides her bike 2 miles to school
each day. She leaves her house at 7:00
and arrives at 7:20. What is Carla’s
average speed in miles per hour?
Learning Target:
I can…
Write expressions involving percents
Writing Expressions
Discount
If p is the original price of an item, write the
expression for a 20% discount.
p – .2p
or
0.8p
Example 2: Discount
If p is the original price of an item, write the
expression for a 15% discount.
Tax
If p is the original price of an item, write the
expression for a total purchase of an item with
3% tax.
p + .03p
or
1.03p
Tax Example 2:
If p is the original price of an item, write the
expression for a 15% discount.
Tax and Discount
If p is the original price of an item, write the
expression for a total purchase of an item with
a 20% discount and a 3% tax.
0.8p + 0.03(0.8p)
1.03p – 0.20(1.03p)