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## 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.

= 8x + 4 = 60
= 8x = 60 - 4
= 8x = 56
= x = 56/8
= x = 7

(b) One-fifth of a number minus 4 gives 3.
= x/5 - 4 = 3
= 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.

= 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.

= 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.

= 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.

= 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.

= 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?

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°).

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?

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?

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?

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?

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
To reach a triple century
You still need forty!

Let the number be x.
= 7x + 90 = 300
= 7x = 300 - 90
= 7x = 210
= x = 210/7
= x = 30
Therefore, the number is 30.