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

(iii) People of Sundargram planted trees in the village garden. Some of the trees were fruit trees. The number of non-fruit trees was 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?

(i) Let Parmit’s marbles equal x.

5 times the number of marbles Parmit has = 5x

5x + 7 = 37

5x = 37 − 7 = 30 (Transposing 7 to R.H.S.)

Dividing both sides by 5,

Therefore, Parmit has 6 marbles.

(ii) Let Laxmi’s age be x years.

3 × Laxmi’s age + 4 = Her father’s age

3x + 4 = 49

3x = 49 − 4 (Transposing 4 to R.H.S.)

3x = 45

Dividing both sides by 3,

x = 15

Therefore, Laxmi’s age is 15 years.

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

3 × Number of fruit trees + 2 = Number of non-fruit trees

3x + 2 = 77

3x = 77 − 2 (Transposing 2 to R.H.S.)

3x = 75

Dividing both sides of the equation by 3,

x = 25

Therefore, the number of fruit trees was 25.