Application of Ratio and
Proportion
Learner’s Module in
Business Mathematics
Quarter 1 ● Module 4 ● Week 4
MHERVIN P. CHULYAO
Developer
Department of Education • Cordillera Administrative Region
NAME: ________________________ GRADE AND SECTION ________________
TEACHER: ____________________ SCORE _____________________________
Republic of the Philippines
DEPARTMENT OF EDUCATION
Cordillera Administrative Region
SCHOOLS DIVISION OF BAGUIO CITY
No. 82 Military Cut-off, Baguio City
Published by:
DepEd Schools Division of Baguio City
Curriculum Implementation Division
Learning Resource Management and Development System
COPYRIGHT NOTICE
2020
Section 9 of Presidential Decree No. 49 provides:
“No copyright shall subsist in any work of the Government of the Philippines.
However, prior approval of the government agency of office wherein the work is
created shall be necessary for exploitation of such work for profit.”
This material has been developed for the implementation of K-12 Curriculum through
the Curriculum Implementation Division (CID)—Learning Resource Management and
Development System (LRMDS). It can be reproduced for educational purposes and
the source must be acknowledged. Derivatives of the work including creating an
edited version, an enhancement or a supplementary work are permitted provided all
original work is acknowledged and the copyright is attributed. No work may be
derived from this material for commercial purposes and profit.
ii
~ DAY 1 ~
What I Know
If you answer all the test items correctly in this pretest, then you may
skip studying this learning material and proceed to the next learning module.
Multiple Choice: Read and understand each item carefully. Choose the letter of the
BEST answer. Write your answers on your answer sheet.
1. Which of the pair of ratios below constitutes a proportion?
A.
B.
₱4
₱ 21
8 in
12 in
and 45 oz
9 oz
21 s
2. Solve
A. 1.6
C.
and 31.5 s
2.6
13
D.
30 ft
and
16 s
21 mi
6h
10.5 ft
and
8s
14.3 mi
3h
8
=𝑛.
B. 4.2
C. 20
D. 40
3. A post 5 m high casts a shadow of 6 m. If the shadow of a nearby tree was
measured to be 24 m, how high is the tree?
A. 20 m
B. 30 m
C. 120 m
D. 144
m
4. Which situation exemplifies an indirect proportion?
A. Area of a cultivated land and the crop harvested.
B. Number of animals in a farm and their food consumption.
C. The population of a country and the area of land per person.
D. Number of weeks and the amount of savings.
5. The law of demand states that: “A higher price typically leads to a lower
quantity demanded.” Thus, the law of demand is classified under which
proportion?
A. Direct
B. Indirect
C. Joint
D. Partitive
6. The law of supply says that: “A higher price typically leads to a higher quantity
supplied.” This is a perfect example of which kind of proportion?
A. Direct
B. Indirect
C. Joint
D. Partitive
7. Good Taste Café and Restaurant donated ₱ 150 000 to three barangays
which are greatly affected by the COVID-19 pandemic in Baguio City.
Fairview Village, City Camp Proper, and Irisan will share the amount in the
ratio 2:3:5. How much will Fairview Village receive?
A. ₱ 30 000
C. ₱ 75 000
B. ₱ 45 000
D. ₱ 100 000
3
8. In a hazmat (hazardous materials) suit factory, 5 tailors can finish 20 suits in
one hour. How long will it take 10 tailors to make 100 suits?
A. ½ h
B. 1 h
C. 2.5 h
D. 5 h
9. Assuming both housekeeping staff work at the same rate, how long will it take
for two housekeeping staff to disinfect an entire quarantine facility area if it
takes 4 days for 8 staff to disinfect it?
A. 8 days
B. 16 days
C. 24 days
D. 32 days
10. A philanthropist promised to donate ₱ 5 for every ₱ 2 contribution received
for the patients of COVID-19. If the total contribution received by the civic
organization is ₱ 120 368, how much will the philanthropist give as donation?
A. ₱ 120 368
C. ₱ 300 920
B. ₱ 240 736
D. ₱ 601 840
11. A farmer wants to plant three times as many rows of cassava and twice as
many rows of corn as he has for peanuts. If he has a total of 264 rows
available, how many rows will he have for corn?
A. 48
B. 72
C. 132
D. 144
12. Dan and Eli are business partners and agreed to share profits and losses
according to their capital ratio. Dan shared ₱ 30 000 while Eli invested
₱ 45 000. In the first month of operation, the net profit amounted to ₱ 18 000.
How much will Eli get from the net profit?
A. ₱ 3 000
B. ₱ 7 200
C. ₱ 9 000
D. ₱ 10 800
13. Which statement is TRUE assuming that a firm has ₱ 900 000.00 current
assets, ₱ 1 200 000.00 total assets, ₱ 300 000.00 current liabilities, and ₱
600 000.00 total liabilities?
A. The firm is incapable of paying its obligations.
B. The firm has ₱ 2 of assets available for every ₱ 1 of its debt.
C. This is a warning to creditors not to lend any amount to the firm.
D. The firm has available ₱ 3 to cover every ₱ 1 of debt.
14. A manufacturing company found that the demand for its product varies
inversely as the price of the product. When the price is ₱ 150, the demand is
500 units. Approximate the demand for a price of ₱ 250.
A. 250 units
C. 300 units
B. 275 units
D. 325 units
15. The Department of Health plans to donate 9 126 bottles of hand sanitizers to
three health care facilities in the ratio of 1 ∶ 3 ∶ 5. The highest number of hand
sanitizers to be given to one of the health care facilities is:
A. 1 014
B. 2 026
C. 3 042
D. 5 070
4
What’s In
In mathematics, you will use ratio and proportion to solve many real-life
problems. Say for instance, in building a sculpture of a famous person, carvers may
use a large model with a ratio of 1:12. So, one inch of the model equals 12 inches or
one foot on the material used in sculpting. They may use proportions to determine
the actual measures of the sculptured figure.
Here is another example we can work on to illustrate the importance of
proportions in some of real-life scenarios.
6 cm
15 cm
http://d68curriculum.weebly.com/uploads/2/1/3/5/21352546/chap07.pdf
The toy car shown on
the left is modeled after a
real car. This will be used by
a petroleum company in their
supercar craze promo. They
are
letting
their
loyal
customers start their own
supercar toy collection.
If
the real car is 5 meters long,
how wide is it?
Solution:
𝑊𝑖𝑑𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑎𝑟 ⟶
𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑎𝑟 ⟶
6 𝑐𝑚
𝑥 𝑚𝑒𝑡𝑒𝑟𝑠
=
→
15 𝑐𝑚
5 𝑚𝑒𝑡𝑒𝑟𝑠
6 𝑐𝑚
𝑥 𝑚𝑒𝑡𝑒𝑟𝑠
=
15 𝑐𝑚 5 𝑚𝑒𝑡𝑒𝑟𝑠
6 ∙ 5 = 15 ∙ 𝑥
Write a proportion
Find the cross product
30 = 15𝑥
Multiply
30 15𝑥
=
15
15
Divide each side by 15
2=𝑥
Simplify
What was shown is just a simple example of real-life situations involving
proportions. As you dig deeper into this module, you will find out that there are other
ways on how to solve proportion problems depending on what type or kind of
proportion is involved. So, let’s get the ball rolling!
5
~ DAY 2 ~
What’s New
Activity #1: Am I Right on the Types?
Direction: Determine the kind of proportion exemplified by each real-life problem.
Write D for direct proportion, I for indirect or inverse proportion, and P for partitive
proportion. Use a separate sheet for your answers and remember not to solve the
problems, instead simply classify each according to the kind of proportion involved.
1. An object that weighs 115 kg on Earth weighs 44 kg on Mars. How much
would a person who weighs 75 kg on Earth weighs on Mars?
2. If a Celsius thermometer reads 100° when a Fahrenheit reads 212°, find the
Celsius reading when the Fahrenheit reading is 32°?
3. When the price is ₱ 150, the demand is 500 units. Approximate the demand
for a price of ₱ 250?
4. When the distance from a source of light is tripled, how does the illumination
change?
5. Demi, a retailer, finds that the sales of face masks run 2:5 as compared to the
sales of face shields. If Demi has ₱ 1 050.00 available for the purchase of
these two items, how much should she spend for face masks?
6. A recipe uses 10 cups of flour for every 4 cups of sugar. If one wants to make
a recipe using 8 cups of flour, how much sugar does one use?
7. The ratio of roses to orchids that Nancy sells is 12:5. If she sold 12 dozen
roses, how many dozens of orchids did she sell?
8. A government agency plans to donate a collection of 9 126 books to three
libraries in the ratio of 1:3:5. How many books will each library get?
9. How much will Nelson’s investment interest will be after two years compared
to five years with a principal of ₱ 150 000.00 at a rate of 2%?
10. Paul plans to have his house be repainted. If it takes 8 hours for 5 people to
paint it, how long would it take 12 people to paint the Paul’s house?
6
What’s In It
REAL-LIFE PROBLEMS INVOLVING PROPORTIONS
Problems involving proportions can be solved easily the moment you are able
to identify what kind of proportion is involved in the given situation. Thus, the next
discussions will deal with solving real-life problems under the different kinds of
proportion.
DIRECT PROPORTION
For two quantities, x and y, an increase in x causes an increase in y as
well. Similarly, a decrease in x causes a decrease in y. In symbols:
𝐱𝟏 𝐱𝟐
=
→ 𝐱 𝟏 𝐲𝟐 = 𝐱 𝟐 𝐲𝟏
𝐲𝟏 𝐲𝟐
Illustrative examples:
1. If you sold 10 laptops which cost ₱ 200 000, then how much do 8 laptops
cost?
Solution:
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑙𝑎𝑝𝑡𝑜𝑝𝑠
𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑠𝑡
10
200 000
=
8
𝑥
10
8
= 200 000 = 𝑥
→ 10𝑥 = 8(200 000)
10𝑥 = 1 600 000
10𝑥
10
=
1 600 000
10
𝑥 = ₱ 160 000
Write a proportion
Find the cross product
Multiply
Divide each side by 10
Simplify
2. It takes Ali 30 minutes to burn 200 calories in a treadmill. How long will it take
for him to burn 800 calories?
Solution:
𝑚𝑖𝑛𝑢𝑡𝑒𝑠
30
𝑥
=
=
⇒ 30(800) = 200𝑥 ⇒ 24 000 = 200𝑥
𝑐𝑎𝑙𝑜𝑟𝑖𝑒𝑠 200 800
𝑥 = 120 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
7
3. An artisan bread maker uses 2 000 grams of flour to make 4 loaves of
handcrafted bread. How many grams of flour is needed to make:
a. 2 loaves of bread?
b. 7 loaves of bread?
Solution:
a.
𝑔𝑟𝑎𝑚𝑠 𝑜𝑓 𝑓𝑙𝑜𝑢𝑟 2 000 𝑥
4 000
=
= ⇒ 𝟒 𝟎𝟎𝟎 = 𝟒𝒙 ⇒ 𝑥 =
𝑙𝑜𝑎𝑣𝑒𝑠 𝑜𝑓 𝑏𝑟𝑒𝑎𝑑
4
2
4
𝒙 = 𝟏 𝟎𝟎𝟎 𝒈𝒓𝒂𝒎𝒔
b.
𝑔𝑟𝑎𝑚𝑠 𝑜𝑓 𝑓𝑙𝑜𝑢𝑟 2 000 𝑥
14 000
=
= ⇒ 1𝟒 𝟎𝟎𝟎 = 𝟒𝒙 ⇒ 𝑥 =
𝑙𝑜𝑎𝑣𝑒𝑠 𝑜𝑓 𝑏𝑟𝑒𝑎𝑑
4
7
4
𝒙 = 3 500 𝒈𝒓𝒂𝒎𝒔
INDIRECT or INVERSE PROPORTION
For two quantities, x and y, an increase in x causes a decrease in y or
vice versa. In symbols:
𝐱 𝟏 𝐲𝟐
=
→ 𝐱 𝟏 𝐲𝟏 = 𝐱 𝟐 𝐲𝟐
𝐱 𝟐 𝐲𝟏
Illustrative examples:
1. It takes 4 mechanics to repair a car for 6 hours, how long will it take for 7
mechanics to do the repair if they work at the same rate?
Solution:
4 𝑚𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑠
4 𝑚𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑠
7𝑚𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑠
=
7𝑚𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑠
𝑥 ℎ𝑜𝑢𝑟𝑠
6 ℎ𝑜𝑢𝑟𝑠
𝑥 ℎ𝑜𝑢𝑟𝑠
= 6 ℎ𝑜𝑢𝑟𝑠
→ 4(6) = 7𝑥
24 = 7𝑥
24
7
24
7
=
Write a proportion
Find the cross product
Multiply
7𝑥
Divide each side by 7
7
3
= 𝑥 𝑜𝑟 𝑥 = 3 7 ℎ𝑜𝑢𝑟𝑠
Simplify
2. In a hazmat (hazardous materials) suit factory, 5 tailors can finish 20 suits in
one hour. How long will it take 10 tailors to make 20 suits?
Solution:
5 𝑡𝑎𝑖𝑙𝑜𝑟𝑠
𝑥 ℎ𝑜𝑢𝑟𝑠
5
1
=
⇒ 5(1) = 10𝑥 ⇒
= 𝑥 𝑜𝑟 𝑥 = ℎ𝑜𝑢𝑟
10 𝑡𝑎𝑖𝑙𝑜𝑟𝑠
1 ℎ𝑜𝑢𝑟
10
2
8
3. It takes 5 hours to cover a certain distance at 60 kph. How long will it take to
cover the same distance at 80 kph?
Solution:
5 ℎ𝑜𝑢𝑟𝑠 80 𝑘𝑝ℎ
300
=
⇒ 5(60) = 80𝑥 ⇒
=𝑥
𝑥 ℎ𝑜𝑢𝑟𝑠 60 𝑘𝑝ℎ
80
3
𝑥 = 3 ℎ𝑜𝑢𝑟𝑠 𝑜𝑟 3 ℎ𝑜𝑢𝑟𝑠 𝑎𝑛𝑑 45 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
4
~ DAY 3 ~
PARTITIVE PROPORTION
Involves identifying parts of a whole based on given ratio of these parts.
Illustrative examples:
1. Divide 430 in the ratio 2 ∶ 3 ∶ 5
Solution:
2 + 3 + 5 = 10
430
10
= 43
2(43) = 86
3(43) = 129
5(43) = 215
Step 1: Add the elements of the ratio
Step 2: Divide the amount by the answer in Step 1
Step 3: Multiply each element of the
ratio by the answer in Step 2
Thus, 86 ∶ 129 ∶ 215 is in the ratio 2 ∶ 3 ∶ 5.
Step 4: Finalize your answer
2. A business’ return of investment will be allocated on three business partners:
John, James, and Jonas in the ratio 3 ∶ 4 ∶ 5. If the total income is ₱ 2 400
000, how much will each receive?
Solution:
3 + 4 + 5 = 12
2 400 000
= 200 000
12
3(200 000) = 600 000 , 4(200 000) = 800 000 , 5(200 000) = 1 000 000
Thus, John gets ₱ 600 000, James receives ₱ 800 000, and Jonas will be left
with ₱ 1 000 000.
9
3. A farmer wants to plant 3 times as many rows of beans and twice as many
rows of corns as he has for strawberries.
a. What is the ratio of beans as to corns as to strawberries?
b. If he has a total of 264 rows, how many rows will he have for each
product?
Solution:
a. 𝑏𝑒𝑎𝑛𝑠 ∶ 𝑐𝑜𝑟𝑛𝑠 ∶ 𝑠𝑡𝑟𝑎𝑤𝑏𝑒𝑟𝑟𝑖𝑒𝑠 ⇒ 2 ∶ 3 ∶ 6
✓ Rows for strawberries is three times that of the rows for beans
✓ Rows for strawberries is twice that of the rows for corns.
b. 2 + 3 + 6 = 11
264
= 24 ⇒ 2(24) = 48 , 3(24) = 72 , 6(24) = 144
11
Thus, 48 rows will be for beans, 72 rows will be allotted for corns, and 144
rows will be used for strawberries.
10
What’s More
Activity #2: Proportion to a Test
Direction: Answer the following problems related to proportion.
complete solution in a separate sheet of paper.
Show your
A. Direct Proportion
1. Three puppies can consume 8 cans of puppy food in a week. How many cans
of puppy food are needed to feed an additional 5 puppies?
2. Carl’s birthday party will cost ₱ 3 920 if she invites 14 guests. If the cost is
directly proportional to the number of invited guests, how much will it cost if she
invites 56 guests?
3. The amount of commission is directly proportional to the amount of sales. A
realtor received a commission of ₱ 180 000 on the sale of a ₱ 2 250 000 house
and lot. How much would the commission be on a ₱ 1 300 000 house and lot?
B. Indirect or Inverse Proportion
1. The number of hours required to do a job is inversely proportional to the number
of people working together. If it takes 8 hours for 5 people to paint a house,
how long would it take 12 people to paint the same house?
2. A manufacturing company found that the demand for its product varies inversely
as the price of the product. When the price is ₱ 150, the demand is 500 units.
Approximate the demand for a price of ₱ 250.
3. Vince and Rain want to play on a seesaw. If Vince weighs 40 kg and is 50 cm
from the fulcrum, how far should Rain sit from the fulcrum if he weighs 33
1
3
kg
to balance the seesaw?
C. Partitive Proportion
1. A business conference was attended by 90 participants, and the ratio of the
number of women to men is 2 ∶ 3. How many men participated in the said
business conference?
2. Paul allocates his monthly salary for bills, food, transportation, and savings at
the ratio of 3 ∶ 3 ∶ 2 ∶ 2. If he received ₱ 28 450 last month, how much did he
spend for his food?
3. The Department of Health plans to donate 9 126 bottles of hand sanitizers to
three health care facilities in the ratio of 1 ∶ 3 ∶ 5. How many bottles of hand
sanitizers will each health care facility receive?
11
~ DAY 4 ~
What I Have Learned
NOTE
Solving problems on proportion requires identifying what kind of proportion you
are working on. Things go on smoothly after, since you know what working equation
or pattern to follow to correctly answer the problems.
Activity #3: Wrap It Up!
Direction: Identify whether each statement is correct or not. Write TRUE if the
statement is correct and write FALSE if it is otherwise. Remember to use a
separate sheet for your answer.
1. Our rule concerning proportions is that “the product of the means equals
the product of the extremes.”
2. X is directly proportional to Y when Y increases in every decrease in X.
3. The price per kilogram of rice and the number of kilograms to buy with
₱ 500 is an example of indirect proportion.
4.
𝐱𝟏
𝐲𝟏
𝐱
= 𝐲𝟐 is a proportion showing direct relationship of two quantities.
𝟐
5. 𝐱 𝟏 𝐲𝟏 = 𝐱 𝟐 𝐲𝟐 is a cross product from two quantities which are inversely
related with each other.
6. A baker uses a ratio of 1 egg for every 4 cups of flour in a certain recipe.
If he uses a dozen of eggs, then he needs 48 cups of flour.
7. When a part of a whole is partitioned into equal or unequal ratios, such
concept involves partitive proportion.
8. A government agency plans to donate a collection of 9 126 books to
three libraries in the ratio of 1:3:5. One of the libraries will receive the
least number of books which is 3 042.
9. Coming up with a budget plan to manage your finances involves direct
proportion.
10. Creating a figure out from a model or prototype involves direct proportion.
12
What I Can Do
Budgeting is a practical money skill. Managing your budget could be stressful
at times as you try to meet ends but should not be taken for granted if you want a
healthy financial future.
Here is a problem we are all familiar with involving one of the kinds of
proportion. Work with it to see how proportion can be related to real-life and reflect
on how have you been managing your finances or your allowance.
Scenario:
The monthly income of a small family amounts to ₱ 30 000.00. This amount
is budgeted on the following: food, rent, bills (city services), transportation, clothing,
recreation, savings, and miscellaneous expenses. The allocation follows the ratio
8:3:2:3:3:2:2:1 respectively.
a. Create a pie graph entitled “Monthly Budget” of the allocation of the
monthly income (as accurate as possible).
b. Give a short description of the created pie chart.
c. How much is allocated to each expense?
d. What can you say with the financial management of the family?
e. What do you suggest to improve their budget plan?
13
~ DAY 5 ~
Post-Assessment
Multiple Choice: Choose the correct answer to each question by writing the letter of
your choice. Remember to write you answers on a separate sheet of paper.
1. A post 5 m high casts a shadow of 6 m. If the shadow of a nearby tree was
measured to be 24 m, how high is the tree?
A. 20 m
B. 30 m
C. 120 m
D. 144 m
2. Solve
2.6
13
8
=𝑛.
A. 1.6
B. 4.2
C. 20
D. 40
3. Which of the pair of ratios below constitutes a proportion?
A.
B.
₱4
9 oz
8 in
21 s
₱ 21
and 45 oz
C.
12 in
and 31.5 s
D.
30 ft
and
16 s
21 mi
6h
10.5 ft
and
8s
14.3 mi
3h
4. Which situation exemplifies an indirect proportion?
A. Area of a cultivated land and the crop harvested.
B. Number of animals in a farm and their food consumption.
C. The population of a country and the area of land per person.
D. Number of weeks and the amount of savings.
5. The law of supply says that: “A higher price typically leads to a higher quantity
supplied.” This is a perfect example of which kind of proportion?
A. Direct
B. Indirect
C. Joint
D. Partitive
6. The law of demand states that: “A higher price typically leads to a lower
quantity demanded.” Thus, the law of demand is classified under which
proportion?
A. Direct
B. Indirect
C. Joint
D. Partitive
7. Good Taste Café and Restaurant donated ₱ 150 000 to three barangays
which are greatly affected by the COVID-19 pandemic in Baguio City.
Fairview Village, City Camp Proper, and Irisan will share the amount in the
ratio 2:3:5. How much will Fairview Village receive?
A. ₱ 30 000
C. ₱ 75 000
B. ₱ 45 000
D. ₱ 100 000
8. In a hazmat (hazardous materials) suit factory, 5 tailors can finish 20 suits in
one hour. How long will it take 10 tailors to make 100 suits?
A. ½ h
B. 1 h
C. 2.5 h
D. 5 h
14
9. Assuming both housekeeping staff work at the same rate, how long will it take
for two housekeeping staff to disinfect an entire quarantine facility area if it
takes 4 days for 8 staff to disinfect it?
A. 8 days
B. 16 days
C. 24 days
D. 32 days
10. A philanthropist promised to donate ₱ 5 for every ₱ 2 contribution received
for the patients of COVID-19. If the total contribution received by the civic
organization is ₱ 120 368, how much will the philanthropist give as donation?
A. ₱ 120 368
C. ₱ 300 920
B. ₱ 240 736
D. ₱ 601 840
11. Dan and Eli are business partners and agreed to share profits and losses
according to their capital ratio. Dan shared ₱ 30 000 while Eli invested
₱ 45 000. In the first month of operation, the net profit amounted to ₱ 18 000.
How much will Eli get from the net profit?
A. ₱ 3 000
B. ₱ 7 200
C. ₱ 9 000
D. ₱ 10 800
12. A farmer wants to plant three times as many rows of cassava and twice as
many rows of corn as he has for peanuts. If he has a total of 264 rows
available, how many rows will he have for corn?
A. 48
B. 72
C. 132
D. 144
13. The Department of Health plans to donate 9 126 bottles of hand sanitizers to
three health care facilities in the ratio of 1 ∶ 3 ∶ 5. The highest number of hand
sanitizers to be given to one of the health care facilities is:
A. 1 014
B. 2 026
C. 3 042
D. 5 070
14. Which statement is true assuming that a firm has ₱ 900 000.00 current
assets, ₱ 1 200 000.00 total assets, ₱ 300 000.00 current liabilities, and ₱
600 000.00 total liabilities?
A. The firm is incapable of paying its obligations.
B. The firm has available ₱ 2 for every ₱ 1 of its debt.
C. This is a warning to creditors not to lend any amount to the firm.
D. The firm has available ₱ 3 to cover every ₱ 1 of debt.
15. A manufacturing company found that the demand for its product varies
inversely as the price of the product. When the price is ₱ 150, the demand is
500 units. Approximate the demand for a price of ₱ 250.
A. 250 units
C. 300 units
B. 275 units
D. 325 units
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Additional Activities
Activity #4: Try More Proportion Problems
Direction: Read and understand the following problems. Use a separate sheet of
paper to organize your solution.
1. Every 3 months, a man deposits in his bank account a savings of ₱ 5 000. In
how many years would he have saved ₱ 250 000.00?
2. A manufacturing company found out that the demand for its product varies
inversely as the price of the product. When the price is ₱ 150, the demand is
1 000 units. What will be the demand for a price of ₱ 250?
3. Apple, carrot, and orange juice are mixed in the ratio 3 ∶ 1 ∶ 2. The volume of
the apple juice is 720 mL.
a. How much more apple juice is used in the mixture than carrot juice?
b. What is the total volume of the juice?
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Activity #5: Managing My Allowance
TASK:
In a short bond paper, create a pie graph entitled “Managing My Weekly
Allowance” showing how you budget your weekly allowance last school
year in our normal set-up. Provide a short description of your graph.
Include a reflection on how have you been managing your weekly
allowance.
RUBRIC
Labels and
Title
Accuracy
Visual
Appearance
Pie Chart
Description
3
2
1
Title is present. All
areas of the graph
are labeled and well
defined including
each sector in the
circle.
The circle of the
circle graph is drawn
correctly. The size of
each sector is
appropriate to the
percent of the circle
that it represents.
Color is used in a
meaningful way. The
graph, title and
labels are arranged
appropriately. Text is
easy to read.
Title is present. Most
areas of the graph
are labeled and well
defined including
most sectors in the
circle.
The circle of the
circle graph is drawn
correctly. The size of
most sectors is
appropriate to the
percent of the circle
that they represent.
Color is used. The
graph, title and
labels are arranged
appropriately. Text
is readable.
Title is missing. Little
or no labeling.
The pie chart is well
explained.
Reflection elaborates
managing one’s
weekly allowance.
The pie chart is
explained with a
reflection on how to
manage one’s
weekly allowance.
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The circle of the circle
graph is not drawn
correctly. The size of
most sectors is not
appropriate to the
percent of the circle
that they represent.
Little or no color used.
The graph, title and/or
labels are not
arranged
appropriately. Text is
missing or difficult to
read.
The pie chart lacks
explanation and
reflection on how to
manage one’s weekly
allowance.
What I Know
1. B
2. D
3. A
4. C
5. B
6. A
7. A
8. C
9. B
10.C
11. B
12. D
13. D
14. C
15. D
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What I Can Do
a.
Monthly Budget
What’s New
Activity #1: Am I Right on the
Types?
1. D 6. D
2. D 7. P
3. I
8. P
4. I
9. D
5. P 10. I
What’s More
Activity 2: Proportion to a
Test
A.
1
3
1. 21 cans
2. ₱ 15 680.00
3. ₱ 104 000.00
B.
1
3
1. 3 hours or 3 hours and 20
minutes
2. 300 units
3. 60 cm
C.
1. 54 men
2. ₱ 8 535.00
3. 1 014 ; 3 042 ; 5 070
respectively
b.
c.
d.
e.
Answers may vary.
Food-₱10 000; Rent-₱3750; Bills-₱2500; Transportation-₱3750;
Clothing-₱3750; Recreation-₱2500; Savings-₱2500;
Miscellaneous-₱1250.
Answers may vary.
Answers may vary.
Post-Assessment
1. A
2. D
3. B
4. C
5. A
6. B
7. A
8. C
9. B
10.C
11. D
12. B
13. D
14. D
15. C
Additional Activities
Activity #4: Try More Proportion Problems
;
What I Have Learned
Activity #3: Wrap It Up!
1. TRUE
6. TRUE
2. FALSE 7. FALSE
3. TRUE
8. FALSE
4. TRUE
9. FALSE
5. TRUE 10. TRUE
1. 12 1/5 years
2. 600 units
3. a. 480 mL
b. 1 440 mL
Activity #5: Managing My Allowance
Answers may vary.
Answer Key
References
Norma D. Lopez-Mariano: Business Mathematics: (Rex Bookstore: First Edition,
April, 2016), 85-95.
Brian Roy C. Lopez, Leah C. Martin-Lundag, and Keneth Adrian P. Dagal: Business
Math: (Vibal Group, Inc.: 2016), 54-70.
Dr. Krongthong Khairiree and Dr. Tran Vui: Discovering Mathematics 2: Problem
Solving Approach: (PADA Education Co., Ltd.: 2014), 1-32.
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For inquiries or feedback, please write or call:
Department of Education – Schools Division of Baguio City
No. 82 Military Cut-off Road, Baguio City
Telefax: 422-4326 / 422-7819
Email Address: depedbaguiocity@gmail.com
Social Media: facebook.com/DepEdTayoBaguioCity
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