## Chapter 4 Simple Equations 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.Answer:**

= 8x + 4 = 60

= 8x = 60 - 4

= 8x = 56

= x = 56/8

= x = 7

**(b) One-fifth of a number minus 4 gives 3.**

Answer:

= x/5 - 4 = 3

Answer:

= x/5 = 3 + 4

= x/5 = 7

= x = 7 × 5

= x = 35

**(c) If I take three-fourths of a number and add 3 to it, I get 21.**

Answer:

Answer:

= 3/4 y + 3 = 21

= 3y/4 = 21 - 3

= 3y/4 = 18

= 3y = 18 × 4

= 3y = 72

= y = 72/3

= y = 24

**(d) When I subtracted 11 from twice a number, the result was 15.**

Answer:

Answer:

= 2m - 11 = 15

= 2m = 15 + 11

= 2m = 26

= m = 26/2

= m = 13

**(e) Munna subtracts thrice the number of notebooks he has from 50, he finds the result to be 8.**

Answer:

Answer:

= 50 - 3x = 8

= -3x = 8 - 50

= -3x = -42

= x = -42/-3

= x = 14

**(f) Ibenhal thinks of a number. If she adds 19 to it and divides the sum by 5, she will get 8.**

Answer:

Answer:

= x + 19/5 = 8

= x + 19 = 8 × 5

= x + 19 = 40

= x = 40 - 19

= x = 21

**(g) Anwar thinks of a number. If he takes away 7 from 5/2 of the number, the result is 23.**

Answer:

Answer:

= 5n/2 - 7 = 23

= 5n/2 = 23 + 7

= 5n/2 = 30

= 5n = 30 × 2

= 5n = 60

= n = 60/5

= n = 12

**Question 2: Solve the following:**

(a) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. What is the lowest score?

Answer:

(a) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. What is the lowest score?

Answer:

Let the lowest score be x.

Highest score is = 87

Highest score = 2x + 7

= 2x + 7 = 87

= 2x = 87 - 7

= 2x = 80

= x = 80/2

= x = 40

Therefore, the lowest score is 40.

**(b) In an isosceles triangle, the base angles are equal. The vertex angle is 40°.**

What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is 180°).

Answer:

What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is 180°).

Answer:

The sum of angles of a triangle = 180°

Let base angle be b.

= b + b + 40° = 180°

= 2b + 40° = 180°

= 2b = 180° - 40°

= 2b = 140°

= b = 140/2

= b = 70°

Therefore, 70° is the base angle of an isosceles triangle.

**(c) Sachin scored twice as many runs as Rahul. Together, their runs fell two short of a double century. How many runs did each one score?**

Answer:

Answer:

Let Rahul’s score be x.

Sachin’s score = 2x

= Rahul’s score + Sachin’s score = 200 - 2

= x + 2x = 198

= 3x = 198

= x = 198/3

= x = 66

Rahul’s score = x = 66

Sachin’s score = 2x = 66 × 2 = 132

Therefore, Rahul’s score is 66 while Sachin’s score is 132.

**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?

Answer:

(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?

Answer:

Let Parmit’s marbles be x.

Irfan’s marbles = 5x + 7

= 5x + 7 = 37

= 5x = 37 - 7

= 5x = 30

= x = 30/5

= x = 6

Therefore, Parmit has 6 marbles.

**(ii) Laxmi’s father is 49 years old. He is 4 years older than three times Laxmi’s age. What is Laxmi’s age?**

Answer:

Answer:

Let Laxmi’s age be y years.

Laxmi’s father age = 3y + 4

= 3y + 4 = 49

= 3y = 49 - 4

= 3y = 45

= y = 45/3

= y = 15

Therefore, Laxmi’s age is 15 years.

**(iii) People of Sundargram planted 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 if the number of non-fruit trees planted was 77?**

Answer:

Answer:

Let the number of fruit trees be x.

Non fruit trees = 3x + 2

= 3x + 2 = 77

= 3x = 77 - 2

= 3x = 75

= x = 75/3

= x = 25

Therefore, number of fruit tree was 25.

**Question 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!

Answer:

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!

Answer:

Let the number be x.

= 7x + 90 = 300

= 7x = 300 - 90

= 7x = 210

= x = 210/7

= x = 30

Therefore, the number is 30.

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