# 2.4 Estimations, equations and variables (algebraic equations)

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## Memorandum

21. (a)

 Days ___ ___ ___ ___ 5 ___ ___ 49 Bo x es ___ ___ 150 200 ___ 600 1 750 ___

22.

(b)

 Sketch ___ ___ ___ ___ ___ ___ Number of squares 4 7 10 13 25 40

(c) Squares = 1 + (Sketch No. x 3)

(d) (i) 1 + (25 x 3) = 76

1. 1 + (37 x 3) = 112
2. 1 + (101 x 3) = 304

(e) (i) 43

1. 55
2. 80

23. (a) u =  i ÷ 4

(b) u = ( i x 2) + 1

24. (a) Input

money

 24. (a) Input money R1 R5 R30 R50 R100 Output : flower bulbs 3 15 90 150 300

(b)

 InputNights 1 7 10 15 31 Output Cost R280 R1 960 R2 800 R4 200 R8 680

(c)

 InputKg 1 2½ 4 5¼ 19 OutputAmount R6,20 R17 R27,70 R35,70 R129,78

## Activity: estimations, equations and variables (algebraic equations) [lo 2.1, lo 2.3.3, lo 2.2, lo 2.4]

21. Let us see if we can formulate rules to solve equations by looking at patterns.

Every day the Cape Market purchases 50 boxes of grapes

from a farmer.

a) Complete the following table:

 Days 1 2 3 4 12 35 Boxes 50 100 250 2 450

b) We can check if you are correct by writing an algebraic equation

for the above:

b (boxes) = d (days) ´ 50

Therefore: c = 3 ´ 50

= 150 (3rd day)

c = d ´ 50

250 = d ´ 50

250 ÷ 50 = d

5 = d

On day 5 the market had already bought 250 boxes of grapes.

c) Work with a partner and check the rest of your work in the same way.

22. Examine the following three sketches:

a) Can you explain to a friend the pattern that is formed here?

b) Complete this table:

 Sketch 1 2 3 4 8 13 Number of squares

c) Can you write down the equation by which you can determine your solution?

_____________________________________________________________________

d) Use your equation to determine the number of squares in

(i) sketch 25: ___________________________________________________

(ii) sketch 37: ___________________________________________________

(iii) sketch 101: ___________________________________________________

e) Which sketches will contain the following number of squares?

(i) 130: _________________________________________________________

(ii) 166: _________________________________________________________

(iii) 241: _________________________________________________________

23. Are you able to write a rule (an algebraic equation) for the relationship between the input and output numbers in the following table?

a)

 Input (i) 16 28 48 60 Output (o) 4 7 12 15

b)

 Input (i) 105 115 125 135 Output (o) 211 231 251 271

24. Compile tables for the following (You may use your pocket calculator):

a) Flower Pot Nursery sells flower bulbs at 3 for a rand. Indicate in your table how many bulbs would be sold for R1,00 ; R5,00 ; R30,00 ; R50,00 and R100,00.

b) The Good Rest Holiday Resort's tariff is R280,00 per person per night. Indicate in your table the cost for one person for the following number of nights: 1 ; 7 ; 10 ; 15 ; 31.

c) At Sally's Supermarket you can buy grapes at R6,80 a kilogram. Indicate in your table how much you would pay for: 1 kg ; 2 ½ kg ; 4 kg ; 5¼ kg ; 19 kg grapes.

25. Time for Self-Assessment

• Make a cross on the scale of 1 to 5 for each of the following:
 Struggling So-so Capable 1 2 3 4 5 I can determine output numbers from a flow diagram correctly __ __ __ __ __ I can determine input numbers from a flow diagram __ __ __ __ __ I understand the replacing of numbers with letters of the alphabet. __ __ __ __ __ I understand what "variables" are. __ __ __ __ __ I understand the replacing of letters of the alphabet with numbers. __ __ __ __ __ I can write algebraic equations for given number sentences. __ __ __ __ __ I can resolve algebraic equations. __ __ __ __ __ I can write number sentences by making use of inequalities. __ __ __ __ __ I am able to formulate rules for solving equations by looking at patterns and can write down equations for them. __ __ __ __ __ I can compile tables from given information. __ __ __ __ __

## Module test

Let us see if we can apply all the previous knowledge.

1. Just write down the answer:

a) 43 = __________ b) 93 = __________ (2)

2. True or false?

a) 125 is a cubed number ________________

b) 125 is a square number ________________

c) v – w = w – v ________________

d) (g + h) x j = (g x j) + (h x j) ________________ (4)

3. If m = 16 ; n = 9 and p = 18, calculate:

a) (m x n) + p ___________________________________

b) p ¸ n x m2 ___________________________________ (2)

4. Write an algebraic equation for the following:

a) If I subtract 347 from a number, the answer is 1706.

______________________________________________ (1)

b) The product of a certain number and 598 is equal to the difference between 80 000 and 6 446

______________________________________________ (2)

5. Write number sentences by using inequalities:

a) One quarter of the red shoes is less than half of the green shoes.

______________________________________________ (1)

b) Everyday more than 100 000 people read the newspaper.

______________________________________________ (1)

6.1 Write an equation for the following table:

 Input 5 10 15 20 25 30 Output 28 53 78 103 128 228 328

______________________________________________ (1)

6.2 Use the equation to complete the table. (3)

7. Compile a table for the following:

At the Happy Fruit Stall you can buy 1 kg of apples for R6,99. In your table, indicate the cost of 2 and a half kg ; 8 kg ; 13 kg (3)

20

## Assessment

Learning Outcome 2: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.

Assessment Standard 2.2: : We know this when the learner describes, explains and justifies observed relationships or rules in own words;

Assessment Standard 2.3: We know this when the learner represents and uses relationships between variables in order to determine input and/or output values in a variety of ways using:

2.3.3: tables;

Assessment Standard 2.4: We know this when the learner constructs mathematical models that represent, describe and provide solutions to problem situations, showing responsibility toward the environment and the health of others (including problems within human rights, social, economic, cultural and environmental contexts).

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