Samples of Comparison Model

Samples of Comparison Samples of Comparison ModelModel

Ex. 1: A sandwich and a soft drink cost P56. If the sandwich costs P8 more than the soft drink, what is the cost of the sandwich?

P8

sandwich P56

soft drink

P56 - =2 units =1 unit =

Therefore, the sandwich costs

P 8

P24

P48

P48

P24P24

modelmodel

Sample of Comparison Sample of Comparison ModelModel

Ex.2: A pencil, pad paper, and eraser cost p42. The paper costs P5 more than the eraser, while the pencil costs P2 more than the paper. Find the cost of each item?

pencilpad of papereraser

P42 - =3 units cost =1 unit cost =

Therefore, the pencil costs , the pad of paper costs , and the eraser costs .

?? P5P5

P5P5????

P2P2

P12P12

P10P10

P30P30

P10P10P17P17 P15P15

P30

P42P42

Your TurnYour Turn

An apple, an orange and a pear costs An apple, an orange and a pear costs P40. A pear costs P5 more than the P40. A pear costs P5 more than the apple, while an orange costs P3 less apple, while an orange costs P3 less than a pear. How much is the cost of than a pear. How much is the cost of each fruit?each fruit? Click for answer

Eureka!!!Eureka!!!

orange orange we subtract 5 & 3 = P13 we subtract 5 & 3 = P13

pearpear = P 16 = P 16

appleapple = P 11 = P 11

P40 – P7 = P33P40 – P7 = P33

3 units cost = P333 units cost = P33

1 unit cost = P111 unit cost = P11

??

??

?? P5P5

P2P2

P40P40

modelmodel

Sample of Sharing ModelSample of Sharing Model

Sammy has 198 marbles and Tony has 74 marbles. Sammy gives some marbles to Tony so that both have the same number of marbles.

a. How many marbles does Sammy have in the end? b. How many marbles does Sammy give Tony?

SammyTony

124 / 2 = 62198 – 62 = 136 marbles were left to Sam orSammy = 74 + 62 = 136. Sammy has 136 marbles at the end.Tony was given 62 marbles.

modelmodel

7474

62

62

124124198198

Your TurnYour Turn

Sammy has 198 sweets and Tony has 74 sweets. Sammy gives some sweets so that he has 12 more sweets than Tony in the end.

a. How many sweets does Sammy have in the end?

b. How many sweets does Sammy give Tony?

modelmodel

Click for answer

Eureka!!!Eureka!!!

SammyTony

198 – 74 = 124124 – 12 = 112112/2 = 56Sammy has 198-56 = 142 sweets.Sammy gave 56 sweets.

modelmodel

7474

7474

5656 56561212

5656

Sample of Constant Value ModelSample of Constant Value Model

Wenie’s age is 42 and her son’s age is 10. In how many years time will

Wenie’s age be twice the age of her son?

42Wenieson

What is double the son’s age today?How many years in excess of the mother’s age is twice the age of the

son?In how many years more will Wenie’s age be twice as that of her son?In 22 years, how old is the mother? the son?In years, Winie’s age is twice her son’s age.

modelmodel

1010 22

2222

2222

2222

2020

6464 3232

2222

22 is the constant value

that we add on both

quantities

Your TurnYour Turn

Racquel’s age is 42 and Anna’s age is 26. How

many years ago was Anna’s age half of

Racquel’s age?

modelmodel

Click for answer

EurekaEureka

modelmodel

RacquelAna

42

26

1052

If years ago, Ana was 26, what must Racquel’s age be during that time?26 x 2 = 52

What’s the difference between the projected age and the present age? 52 – 42 = 10

We want to know the number of years ago. Subtract 10 from each.42 -10 = 3226 - 10 = 16

Ten years ago, Ana’s age was half of Racquel’s age.

26-10=16

42-10 = 32 10

10

Go For Gold!Go For Gold!

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Learn More ExamplesLearn More Examples““Practice makes perfect.”Practice makes perfect.”

2. Allan has 55 marbles and Jessica has 87 marbles. How many marbles must Jessica give to Allan so that they will have the same number of marbles?


2. Allan has 55 marbles and Jessica has 87 marbles. How many marbles must Jessica give to Allan so that they will have the same number of marbles?

55AllanAllan

JessicaJessica

32 pupils32 pupils

87 – 55 = 3287 – 55 = 32

32/2 = 1632/2 = 16

Jessica must give 16 marbles to Allan.Jessica must give 16 marbles to Allan.


3. Anthony buys two hamburgers and 3 cans of juice for P121. Each can of juice costs three times as much as one hamburger. How much more does each can of juice cost than each hamburger?


3. Anthony buys two hamburgers and 3 cans of juice for P121. Each can of juice costs three times as much as one hamburger. How much more does each can of juice cost than each hamburger?

Cans of juiceCans of juice

hamburgerhamburgerP121P121

11 units = 121;11 units = 121; 1 unit = 111 unit = 11

3 units = 333 units = 33

Each can of juice is P22more than the hamburgerEach can of juice is P22more than the hamburger

A difference between each item cost is P33-P11= P22.A difference between each item cost is P33-P11= P22.


4. John had P45 and William had P120. One day Mr. Enriquez gave John and William an equal amount of money. After that, John had half the amount of money as William. How much money did Mr. Enriquez give them altogether?


4. John had P45 and William had P120. One day Mr. Enriquez gave John and William an equal amount of money. After that, John had half the amount of money as William. How much money did Mr. Enriquez give them altogether?

JohnJohn

WilliamWilliam

P120P120

120- (2x45) = 30; 120- (2x45) = 30;

Mr. Enriquez gave P30 to each. Altogether, he gave P60.Mr. Enriquez gave P30 to each. Altogether, he gave P60.

4545

4545 4545 3030 3030

3030

45 is half of 90; 45 is half of 90; 30 is the excess; the constant value 30 is the excess; the constant value

Add 30 to both quantities to satisfy the condition. Add 30 to both quantities to satisfy the condition.


5. Tomas is twice as tall as Ronald. Ronald is 25 cm shorter than Armand. Their total height is 345 cm. Find the height of Tomas.


5. Tomas is twice as tall as Ronald. Ronald is 25 cm shorter than Armand. Their total height is 345 cm. Find the height of Tomas.

TomasTomas

RonaldRonald 345345

4 units + 25 = 3454 units + 25 = 345

Tomas is 160 cm tallTomas is 160 cm tall

4 units = 3204 units = 320

ArmandArmand

2525

1 unit = 801 unit = 80

Stretch Your Mind Stretch Your Mind

3. Benson is three times as old as Daryl. Ed is 8 years older than Daryl. The sum of their ages is 78 years. How old is each?

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GoldGold


4. The number of students in ABC National High School is 40 less than thrice the number of students XYZ National High School. The total number of students in both schools is 5440. How many students does each school have?

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6. The sum of two numbers is 31 and their difference is 5. What are the two numbers?

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GoldGold


7. Manny and Joseph have 98 cards and 164 respectively. Joseph gives some cards to Manny. If Manny has 10 more cards than Joseph in the end, find the number of cards each of them have in the end?

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GoldGold

Count Your TreasuresCount Your Treasures

These are the answers to the given exercises.

3.3. Daryl is 14 years old. Benson is 42 years old. Ed is 22 years old.Daryl is 14 years old. Benson is 42 years old. Ed is 22 years old.

BensonBenson

5 units + 8 years = 78 years5 units + 8 years = 78 years

5 units = P705 units = P70

1 unit = 70 /51 unit = 70 /5

DarylDaryl

8EdEd

78 years

1 unit = 14 years1 unit = 14 years

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4.4. ABC School has 4 070 students and XYZ School has 1370 students.ABC School has 4 070 students and XYZ School has 1370 students.

ABCABC

4 units - 40 students = 5440 students4 units - 40 students = 5440 students

4 units = 5 4804 units = 5 480

1 unit = 1 370 1 unit = 1 370

XYZXYZ

40

5 440 years

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6.6. The two numbers are 13 and 18.The two numbers are 13 and 18.

31 - 5 = 2631 - 5 = 26

2 units = 622 units = 62

1 unit = 131 unit = 13

3131First numberFirst number

Second numberSecond number

55

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7.7.Joseph will have 126 cards and Manny will have 136.Joseph will have 126 cards and Manny will have 136.

164 - 98 = 66164 - 98 = 66

66 - 10 = 5666 - 10 = 56

56/2 = 2856/2 = 28

9898MannyManny

JosephJoseph

6666

282810102828

28 + 10 will be added to Manny.28 + 10 will be added to Manny.

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Samples of Comparison Model

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