Name:________________________________________________________________________________Date:_____/_____/__________
1)
Define proportion in your own words.
QUIZ
DAY!
Do the following ratios form a proportion? (Yes or No)
2)
13
5
=
8
3
3)
3
5
=
9
15
Solve the following scenarios using a proportion (round to
the nearest whole number when necessary) :
Remember: Cross-multiply first, then DIVIDE by coefficient!
4) The ratio of pencils to pens is
9 : 5. If there are 23 pencils,
approximately how many pens
are there?
Set up PROPORTION and solve:
5) For every 3 ducks, there are 8
geese at the pond. If there are 24
geese at the pond, how many
TOTAL ducks and geese are
there?
Set up PROPORTION and solve:
=
=
Solve the following “scale” problems using a proportion:
6) The scale on a map is . . .
2.5 inches = 15 miles
Set up PROPORTION and solve:
=
If two towns are 6 in apart on map,
what is their actual distance?
7) 1 cm on the blueprint represents
12 ft in real life. If the living room
is 15 ft in real life, what is its
blueprint measurement?
Set up PROPORTION and solve:
=
Today’s Lesson:
What:
Percentage applications
Why:
To solve several different types of
percentage problems, including consumer
applications, using the percent proportion
formula.
The Percent proportion formula . . .
%
100
=
part “is”
whole “of”
We can use the above formula to solve ANY
type of percentage problem. WHY???
Because, using this formula allows us to find
the missing percentage, find the missing
part, or find the missing
whole
_________________________.
x (variable) in the correct
We place ____________
position, according to what we need to find.
How do we set the proportion up???
Like this . . .
5 out of 85 is what percent?
𝒙
𝟓
=
Solving for the
percent . . .
𝟏𝟎𝟎
𝟖𝟓
Find 25% of 75:
𝟐𝟓
𝒙
=
𝟏𝟎𝟎
𝟕𝟓
Solving for the
part . . .
20 is 10% of what number?
𝟏𝟎
𝟐𝟎
=
𝟏𝟎𝟎
𝒙
Solving for the
whole . . .
%
100
=
part “is”
whole “of”
%
100
=
part “is”
whole “of”
Real-Life Scenarios:
1)
Collin scored an 88% on the test. If
there were 40 total questions, how
many did Collin answer correctly?
x ≈ 35 questions
%
100
=
part “is”
whole “of”
2) Jane scored a 94% on the test. If she
answered 47 questions correctly, how
many total questions were on the test?
x = 50 questions
%
100
=
part “is”
whole “of”
3) On the Unit 8 Test, Holly got 40 questions
correct out of 45 total questions. What
was her percentage score?
x ≈ 89%
Consumer applications . . .
A consumer is someone who
purchases
__________________________
goods/ services
at a variety of stores/businesses.
Things for a consumer to consider are:
Taxes (_________
to the purchase)
add
subtract from the purchase)
Discounts (____________
Tips (__________
to the purchase)
add
Using the percent proportion formula--tax,
discount, and tip problems always involve
finding the
So, x will
always be in the _________
part position!
%
100
part “is”
whole “of”
=
Tip: Add
Discount: Subtract
Tax: Add
Store Scenarios:
1) The sub-total (original price) of your
purchase is $54.50. There is a 30%
discount. What is the sale price?
Sale price
means price
AFTER the
discount, so this
is a TWO-STEP
problem.
Step 2: Subtract the discount!
Step 2: Subtract discount
from original amount!
Step 1:
𝟑𝟎
𝟏𝟎𝟎
Step 1: Find the discount using
the % proportion.
=
𝒙
𝟓𝟒.𝟓
1,635 = 100x
100
100
$54.50 - $16.35 = $38.15
x = $16.35
$38.15
%
100
=
part “is”
whole “of”
Tip: Add
Discount: Subtract
Tax: Add
2) The sub-total (original price) of your
purchase is $98.25. There is a 5% sales
tax. What is the tax only?
This is asking for
tax only, so it
just a ONE-STEP
problem!
$4.91
%
100
=
part “is”
whole “of”
Tip: Add
Discount: Subtract
Tax: Add
3) The sub-total (original price) of your
purchase is $74.80. The sales tax is 5%.
What is your total?
This is asking for
the TOTAL, so it
is a 2-step
problem!
$78.54
%
100
Tip: Add
Discount: Subtract
Tax: Add
=
part “is”
whole “of”
Restaurant scenarios:
1) Your bill at a restaurant is $26.00. You want
to leave a 15% tip. How much is the tip?
This is asking for
the TIP only, so
it is a ONE-STEP
problem!
$3.90
%
100
Tip: Add
Discount: Subtract
Tax: Add
=
part “is”
whole “of”
5) Your bill at a restaurant is $44.00. You
want to leave an 18% tip. How much is
the total bill?
This is asking for
the TOTAL, so it
is a TWO-STEP
problem!
$51.92
END OF LESSON
The next slides are student copies of the notes and
handouts for this lesson. These were handed out in
class and filled-in as the lesson progressed.
NAME:
What:
Why:
DATE: ______/_______/_______
Math-7 NOTES
percentage applications
To solve several different types of percentage problems, including consumer applications,
using the percent proportion formula.
The Percent proportion formula . . .
%
100
=
part “is”
whole “of”
We can use the above formula to solve ANY type of percentage problem.
WHY??? Because, using this formula allows us to find the missing percentage,
find the missing part, or find the missing _________________________.
We place _________ in the correct position, according to what we need to find.
How do we set the proportion up??? Like this . . .
Solving for the
percent . . .
5 out of 85 is what percent?
𝒙
𝟓
=
𝟏𝟎𝟎
𝟖𝟓
Find 25% of 75:
𝟐𝟓
𝟏𝟎𝟎
=
Solving for the
part . . .
𝒙
𝟕𝟓
20 is 10% of what number?
𝟏𝟎
𝟏𝟎𝟎
=
𝟐𝟎
𝒙
Solving for the
whole . . .
%
100
=
part “is”
whole “of”
Real-Life Scenarios:
1) Collin scored an 88% on the test. If there were 40 total questions, how
many did Collin answer correctly?
2)
Jane scored a 94% on the test. If she answered 47 questions correctly, how
many total questions were on the test?
3)
On the Unit 8 Test, Holly got 40 questions correct out of 45 total questions.
What was her percentage score?
Consumer applications . . .
A consumer is someone who __________________________ goods/ services at
a variety of stores/businesses.
Things for a consumer to consider are:
Taxes (_________ to the purchase)
Discounts (____________ from the purchase)
Tips (__________ to the purchase)
Using the percent proportion formula--tax, discount, and tip problems always
involve finding the
So, x will always be in the _________
position!
%
100
=
part “is”
whole “of”
Store and Restaurant Scenarios:
1)
Tip: Add
Discount: Subtract
Tax: Add
The sub-total (original price) of your purchase is $54.50. There is a 30%
discount. What is the sale price?
2) The subtotal (original price) of your purchase is $98.25. There is a 5% sales
tax. What is the tax only? (Hint: one-step problem . . .)
3)
The sub-total (original price) of your purchase is $74.80. The sales tax is
5%. What is your total? (Hint: two-step problem . . .)
4)
Your bill at a restaurant is $26.00. You want to leave a 15% tip. How much is
the tip? (Hint: one-step problem . . .)
5)
Your bill at a restaurant is $44.00. You want to leave an 18% tip. How much
is the total bill (after the tip)? (Hint: two-step problem . . .)
NAME:____________________________________________________________________________
DATE: ______/_______/_______
“Percent Proportions”
Use the Percent Proportion Formula to answer the following (some do
not work out evenly– round to the nearest tenth unless otherwise
specified) :
1) Bridget scored a 95% on the test. If there
were 40 questions, how many did she answer
correctly?
2) Zack scored a 92% on the test. If he
answered 23 questions correctly, how many
total questions were on the test?
3) Linda got 33 questions correct out of 40
total questions on the test. What is her
percentage score (round to the nearest
whole percent)?
4) Nate had $50 in his piggy bank. He took
$22 out in order to buy some headphones.
What percent of his original total did he take
out?
5) Sandy withdrew 34% of her savings.
If she withdrew $120, how much was in her
savings to begin with?
%
100
=
𝑝𝑎𝑟𝑡
𝑤ℎ𝑜𝑙𝑒
“consumer applications”
Read the situations below, identify what type of consumer math (tax, tip, discount) and
tell whether the final price would increase (you would add) or the price would decrease
(you would subtract):
Situation
Type of problem
1.
Leigh just got her haircut and styled. She
paid the price, and then paid her stylist an
additional 20%.
2.
Hector purchased a new video game at
Target for 20% off the original price.
3.
Ms. Yorty purchased new pencils for all her
students. She was charged an additional
4.5% on top of the price of the pencils.
Solve:
4. The original price of a jacket is
5.
$74.00. What is the total cost of the
jacket if it is on sale for 30% off?
6.
The sub-total at Target is $88.90. If 7.
there is a 6% sales tax, how much
is the tax only?
Increase or Decrease?
James and his family went out to
dinner. Their bill was $48.50. If
they gave a 20% tip, what was their
total?
Your family goes out to dinner, and
the bill is $54.00. You offer to leave
the tip. If you leave 15%, how
much did you leave?