Solving problems involving linear inequalities in two variables

Nov 25, 2018Download as pptx, pdf23 likes37,760 views

This document discusses solving problems involving linear inequalities in two variables. It begins by stating the learning objectives, which are to solve such problems and appreciate their use in real-life situations. An activity is presented involving using a budget to purchase ingredients for chicken adobo. Students are asked to model word problems using linear inequalities with two variables. Examples are provided and students practice translating situations into inequalities. The document solves sample problems and discusses using inequalities to represent real-life scenarios. Students are ultimately tasked with finding examples of such situations from their own experiences.

LEARNING OBJECTIVE:
Solves problems involving linear inequalities
in two variables. (M8AL-IIa- 4)

SPECIFIC OBJECTIVES:
1. Translate mathematical statements into linear
inequalities in two variables.
2. Solve problems involving linear inequalities in
two variables.
3. Appreciate the importance of using inequalities
in real-life situations.

ACTIVITY 1( BUDGET MATTERS)
Directions: Use the situation below to answer the
question below.
Amelia was given by her mother Php320 to
buy some food ingredients for “chicken adobo”. She
made sure that it is good for 5 people.

1. Suppose you were Amelia. Complete the following
table with the needed data.
INGREDIENTS QUANTITY COST PER UNIT OR
PIECE
ESTIMATED COST
Chicken 1 kl Php150 Php150
Soy sauce 1 pack Php8 Php8
vinegar 1 pack Php6 Php6
garlic 1 cloves Php5 Php5
onion 2 pcs. Php3 Php6
Black pepper 3 small packs Php1 Php3
sugar ¼ kl Php50 Php12.50
tomato 3 pcs Php3 Php9
Green pepper 2 mini packs Php1 Php2
potato ¼ kl Php80 Php20

Process questions:
1. How do you feel while budgeting the amount of
Php320 given by the mother of Amelia to buy
ingredients for “Chicken Adobo”?
2. What is the total amount of the estimated cost for
“chicken adobo”?
3. What can you say about Amelia?
4. Compare the amount of money given to Amelia and the
estimated cost she used for ingredients for “chicken
adobo”?

Certain situations in real life can
be modeled by linear inequalities.

Examples:
1. The total amount of 1-peso coins and
5-peso coins of Pedro in his bag is more
than Php150.
2. Emily bought two blouse and a pair of
pants. The total amount she paid for the
items is not more than Php980.

How are we going to translate
statements into linear inequality in two
variables?

1. The total amount of 1-peso coins and
5-peso coins of Pedro in his bag is more
than Php150.
This can be modelled as 𝑥 + 5𝑦 > 150
where 𝑥 is the number of 1 −peso coins
and 𝑦 is the number of 5 − peso coins.

2. Emily bought two blouse and a pair of
pants. The total amount she paid for the
items is not more than Php980.
This can be modeled as 2𝑥 + 𝑦 ≤ 980,
where 𝑥 is the cost of each blouse and 𝑦 is
the cost of pair of pants.

Translate Me!
1. The sum of 20 − peso bills (t) and fifty
peso bills (f) is greater than Php420.
20𝑡 + 50𝑓 > 420

2. The difference between the weight
of Diana (d) an Princess (p) is at least
26
𝑑 − 𝑝 ≤ 26

3. The number of kalape (k) more
than twice the number of igot (i) is
greather than 24
2𝑖 + 𝑘 > 24

Process questions:
1. How did you translate the given situations into linear
inequalities?
2. When do we use the term “at most”? How about “at
leatst”?
3. What other terms are similar to “at most”? How about “
at least”?
4. In what real-life situations are terms such as “at most”
and “at least “ used?

Now let us solve problems involving linear
inequalities.
1. The difference between Aljun’s height and Janel’s height is
not more than 1.5 ft.
a. What mathematical statement represents the difference in
the height of Aljun and Janel? Define the variables used?
let x be Aljun’s height and y be Janel’s height
𝑥 − 𝑦 ≤ 1.5

b. Based on the mathematical statement you have
given, who is taller? Why?
c. Suppose Aljun’s height is 5 ft and 3 in, what
cound be the height of Janel? Explain you answer

Evaluation: Make it Real!
Directions: Each group will be given
strip of paper with a situational real-life
problem on linear inequalities. Give
your complete solutions or
explanations.

Assignment
Determine at least 3 real-life situations
you have encounter that uses linear
inequalities. Write it in you Activity
notebook.

Thank you so much for listening and
cooperating today

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Solving problems involving linear inequalities in two variables

1. SOLVING PROBLEMS INVOLVING LINEAR INEQUALITIES IN TWO VARIABLES.

2. LEARNING OBJECTIVE: Solves problems involving linear inequalities in two variables. (M8AL-IIa- 4)

3. SPECIFIC OBJECTIVES: 1. Translate mathematical statements into linear inequalities in two variables. 2. Solve problems involving linear inequalities in two variables. 3. Appreciate the importance of using inequalities in real-life situations.

4. ACTIVITY 1( BUDGET MATTERS) Directions: Use the situation below to answer the question below. Amelia was given by her mother Php320 to buy some food ingredients for “chicken adobo”. She made sure that it is good for 5 people.

5. 1. Suppose you were Amelia. Complete the following table with the needed data. INGREDIENTS QUANTITY COST PER UNIT OR PIECE ESTIMATED COST Chicken 1 kl Php150 Php150 Soy sauce 1 pack Php8 Php8 vinegar 1 pack Php6 Php6 garlic 1 cloves Php5 Php5 onion 2 pcs. Php3 Php6 Black pepper 3 small packs Php1 Php3 sugar ¼ kl Php50 Php12.50 tomato 3 pcs Php3 Php9 Green pepper 2 mini packs Php1 Php2 potato ¼ kl Php80 Php20

6. Process questions: 1. How do you feel while budgeting the amount of Php320 given by the mother of Amelia to buy ingredients for “Chicken Adobo”? 2. What is the total amount of the estimated cost for “chicken adobo”? 3. What can you say about Amelia? 4. Compare the amount of money given to Amelia and the estimated cost she used for ingredients for “chicken adobo”?

7. Certain situations in real life can be modeled by linear inequalities.

8. Examples: 1. The total amount of 1-peso coins and 5-peso coins of Pedro in his bag is more than Php150. 2. Emily bought two blouse and a pair of pants. The total amount she paid for the items is not more than Php980.

9. How are we going to translate statements into linear inequality in two variables?

10. 1. The total amount of 1-peso coins and 5-peso coins of Pedro in his bag is more than Php150. This can be modelled as 𝑥 + 5𝑦 > 150 where 𝑥 is the number of 1 −peso coins and 𝑦 is the number of 5 − peso coins.

11. 2. Emily bought two blouse and a pair of pants. The total amount she paid for the items is not more than Php980. This can be modeled as 2𝑥 + 𝑦 ≤ 980, where 𝑥 is the cost of each blouse and 𝑦 is the cost of pair of pants.

12. Translate Me! 1. The sum of 20 − peso bills (t) and fifty peso bills (f) is greater than Php420. 20𝑡 + 50𝑓 > 420

13. 2. The difference between the weight of Diana (d) an Princess (p) is at least 26 𝑑 − 𝑝 ≤ 26

14. 3. The number of kalape (k) more than twice the number of igot (i) is greather than 24 2𝑖 + 𝑘 > 24

15. Process questions: 1. How did you translate the given situations into linear inequalities? 2. When do we use the term “at most”? How about “at leatst”? 3. What other terms are similar to “at most”? How about “ at least”? 4. In what real-life situations are terms such as “at most” and “at least “ used?

16. Now let us solve problems involving linear inequalities. 1. The difference between Aljun’s height and Janel’s height is not more than 1.5 ft. a. What mathematical statement represents the difference in the height of Aljun and Janel? Define the variables used? let x be Aljun’s height and y be Janel’s height 𝑥 − 𝑦 ≤ 1.5

17. b. Based on the mathematical statement you have given, who is taller? Why? c. Suppose Aljun’s height is 5 ft and 3 in, what cound be the height of Janel? Explain you answer

18. Evaluation: Make it Real! Directions: Each group will be given strip of paper with a situational real-life problem on linear inequalities. Give your complete solutions or explanations.

19. Assignment Determine at least 3 real-life situations you have encounter that uses linear inequalities. Write it in you Activity notebook.

21. Thank you so much for listening and cooperating today

Solving problems involving linear inequalities in two variables

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Solving problems involving linear inequalities in two variables