# 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 the number, you get 60.

Answer: If number is x then,
8x + 4 = 60
Or, 8x = 60 – 4 = 56
Or, x = 56 ÷ 8 = 7

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

Answer: If the number is x then,
x/5 – 4 = 3
Or, x/5 = 3 + 4 = 7
Or, x = 7 xx 5 = 35

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

Answer: (3x)/(4) + 3 = 21
Or, (3x)/(4) = 21 – 3 = 18
Or, 3x = 18 xx 4 = 72
Or, x = 72 ÷ 3 = 24

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

Answer: 2x – 11 = 15
Or, 2x = 15 + 11 = 26
Or, x = 26 ÷ 2 = 13

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

Answer: 50 – 3x = 8
Or, 3x = 50 – 8 = 42
Or, x = 42 ÷ 3 = 14

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

Answer: (x + 19)/(5) = 8
Or, x + 19 = 8 xx 5 = 40
Or, x = 40 – 19 = 21

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

Answer: (5x)/(2) – 7 = 23
Or, (5x)/(2) = 23 + 7 = 30
Or, 5x = 30 xx 2 = 60
Or, x = 60 ÷ 6 = 12

Question 2: Solve the following:

1. 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: If lowest marks = x
Then, 2x + 7 = 87
Or, 2x = 87 – 7 = 80
Or, x = 80 ÷ 2 = 40
2. 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: Let us assume that a base angle = x
Then, 2x + 40 = 180
Or, 2x = 180 – 40 = 140
Or, x = 140 ÷ 2 = 70°
3. 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: If Rahul’s score = x then Sachin’s score = 2x
Then, x + 2x = 200 – 2 = 198
Or, 3x = 198
Or, x = 198 ÷ 3 = 66
Rahul’s score = 66
Sachin’s score = 132

Question 3: Solve the following:

1. 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 us assume that number of marbles with Parmit = x
Then, 5x + 7 = 37
Or, 5x = 37 – 7 = 30
Or, x = 30 ÷ 5 = 6
2. Laxmi’s father is 49 years old. He is 4 years older than three times Laxmi’s age. What is Laxmi’s age?

Answer: Let us assume Laxmi’s age = x
Then, 3x + 4 = 49
Or, 3x = 49 – 4 = 45
Or, x = 45 ÷ 3 = 15
3. 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: Let us assume that number of fruit trees = x
Then, 3x + 2 = 77
Or, 3x = 77 – 2 = 75
Or, x = 75 ÷ 3 = 25

Question 4: Solve the following riddle:

I am a number,
Tell my identity!
Take me seven times over,
Answer: Let us assume the number = x
Then, 7x + 50 = 300 – 40 = 260
Or, 7x = 260 – 50 = 210
Or, x = 210 ÷ 7 = 30