Class 7 Maths

Simple Equations NCERT 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:

(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: If lowest marks = x

Then, 2x + 7 = 87

Or, 2x = 87 – 7 = 80

Or, x = 80 ÷ 2 = 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: Let us assume that a base angle = x

Then, 2x + 40 = 180

Or, 2x = 180 – 40 = 140

Or, x = 140 ÷ 2 = 70°

(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: 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:

(a) 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

(b) 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

(c) 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