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**Exercise 4.3 ****Ques 1: ****Solve the following equations: **

**Ans: ****(a) **

(b) 8t+28 = 10

**Ques 2: ****Solve the following equations: ****(a) 2(x + 4) = 12****(b) 3(n - 5) = 21****(c) 3(n - 5) = -21 ****(d) 3-2(2 - y) = 7****(e) -4(2 - x) = 9****(f) 4(2 - x) = 9****(g) 4 + 5(p - 1) = 34****(h) 34 - 5(p - 1) = 4****Ans: ****Ques 3: ****Solve the following equations: ****(a) 4 = 5(p - 2)****(b) -4 = 5(p - 2)****(c) -16 = -5(2 - p)****(d) 10 = 4 + 3(t + 2)****(e) 28 = 4 + 3(t + 5)****(f) 0 = 16 + 4(m - 6)****Ans:****(a) **4 = 5 (p-2)

**Ques 4: ****(a) Construct 3 equations starting with x = 2. ****(b) Construct 3 equations starting with x = -2. ****Ans: ****(a) 3** equations starting with x = 2.

(i) x = 2

Multiplying both sides by 10,

10* = 20

Adding 2 both sides 10x+2 = 20+2 = 10x+ 2 = 22

(ii) x = 2

Multiplying both sides by 5

5x = 10

Subtracting 3 from both sides

5x-3 = 10-3 = 5x-3 = 7

(iii) x = 2

Dividing both sides by 5

x/5 = 2/5

**(b)** 3 equations starting with x = -2.

(i) x = -2

Multiplying both sides by 3 3x - -6

(ii) x = -2

Multiplying both sides by 3

3x = -6

Adding 7 to both sides

3x+7 = -6+7 = 3x+7 = 1

(iii) x = -2

Multiplying both sides by 3

3x = -6

Adding 10 to both sides

3x + 10 = -6 + 10 = 3x+10 = 4**Exercise 4.4 ****Question 1: Set up equations and solve them to find the unknown numbers in the following cases:****(a) Add 4 to eight times a number; you get 60. ****(b) One-fifth of a number minus 4 gives 3. ****(c) If I take three-fourth of a number and add 3 to it, I get 21. ****(d) When I subtracted 11 from twice a number, the result was 15. ****(e) Munna subtracts thrice the number of notebooks he has from 50, he finds the result to be 8. ****(f) Ibenhal thinks of a number. If she adds 19 to it divides the sum by 5, she will get 8. ****(g) Answer thinks of a number. If he takes away 7 from 5/2 of the number, the result is 11/2 ****Ans: ****(a) **Let the number be x.

According to the question, 8x + 4 = 60

(b) Let the number be y.

According to the question,

(c) Let the number be z.

According to the question,

(d) Let the number be x.

According to the question, 2x -11 = 15

â‡’ 2x = 15 +11

â‡’ 2x = 26

â‡’ x = 26/2

â‡’ x = 13

(e) Let the number be m.

According to the question, 50-3/m = 8

â‡’ -3m = 8-50

â‡’ -3m = -42

â‡’ m = -42/-3

â‡’ m = 14

(f) Let the number be n.

According to the question,

â‡’ n + 19 = 8x5

â‡’ n + 19 = 40

â‡’ n = 40 - 19

â‡’ n = 21

(g) Let the number be x.

According to the question,

**Question 2: ****Solve the following: ****(a) The teacher tells the class that the highest marks obtained by a student in her class are twice the lowest marks plus 7. The highest score is 87. What is the lowest score? ****(b) In an isosceles triangle, the base angles are equal. The vertex angle is 40 ^{o}. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is 180^{o.} ) **

According to the question, 2y + 7 = 87

â‡’ 2y + 7 = 87

â‡’ 2y = 80

â‡’ y = 80/2

â‡’ y = 40

**(b) **Let the base angle of the triangle be b.

Given, a = 40Â°, b = c

Since, a + b +c = 180Â° [Angle sum property of a triangle]

â‡’ 40Â° + 6 + 6 = 180Â°

â‡’ 40Â°+26 = 180Â°

â‡’ 26 = 180Â°- 40Â°

â‡’ 26 = 140Â°

â‡’ b = 140Â°/2

â‡’ b = 70Â°

Thus, the base angles of the isosceles triangle are 70Â° each.

(c) Let die score of Rahul be x runs and Sachin's score is 2x.

According to the question, x + 2x = 198

â‡’ 3x = 198

â‡’ x = 198/3

â‡’ x = 66

Thus, Rahul's score = 66 runs

And Sachin's score = 2x66 = 132 runs.**Question 3: ****Solve the following: ****(i) Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. How many marbles does Parmit have? ****(ii) Laxmiâ€™s father is 49 years old. He is 4 years older than three times Laxmiâ€™s age. What is Laxmiâ€™s age? ****(iii) People of Sundergram planted a total of 102 trees in the village garden. Some of the trees were fruit trees. The number of non-fruit trees were two more than three times the number of fruit trees. What was the number of fruit trees planted?****Ans: ****(i) **Let the number of marbles Parmit has be m.

According to the question, 5m + 7 = 37

â‡’ 5m = 37-7

â‡’ 5m = 30

â‡’ m = 30/5

â‡’ m = 6

Thus, Parmithas 6 marbles.

(ii) Let the age of Laxmi be y years.

Then her father's age = (3y + 4) years

According to question, 3y + 4 = 49

â‡’ 3y = 49-4

â‡’ 3y = 45

â‡’ y = 45/3

â‡’ y = 15

Thus, the age of Laxmi is 15 years.

(iii) Let the number of fruit trees be t.

Then the number of non-fruits tree = 3t + 2

According to the question, t + 3t + 2 = 102

â‡’ 4t + 2 = 102

â‡’ 4t = 102-2

â‡’ 4t = 100

â‡’ t = 100/4

â‡’ t = 25

Thus, the number of fruit trees are 25.**Ques 4: ****Solve the following riddle: ****I am a number, ****Tell my identity! ****Take me seven times over, ****And add a fifty! ****To reach a triple century, ****You still need forty! ****Ans: **Let the number be n.

According to the question, 7n + 50 + 40 = 300

â‡’ 7n + 90 = 300

â‡’ 7n = 300-90

â‡’ 7n = 210

â‡’ n = 210/7

â‡’ n = 30

Thus, the required number is 30.

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