Exercise 4.3

1. Set up equations and solve them to find the unknown numbers in the following cases:

Instruction

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?

Solution:

Let lowest score be m.

Given: Twice the lowest score + 7 = Highest mark

× m + 7 =

To isolate m, subtract on both sides.

2m + 7 - 7 = 87 - 7 which gives 2m =

Divide by on both the sides.

m =

(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°).

Solution:

Let base angle 1 = base angle 2 = b

Given: vertex angle = 40°

b + b + = °

To isolate b, subtract on both sides.

2b + 40 - 40 = 180° - 40° which gives us 2b = °

Dividing by on both the sides.

b = °

(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?

Solution:

Let Rahul's runs be r.

Given: Sachin score =

r + 2r3r = -

=

Divide by on both the sides.

r = runs

Thus, Rahul scored 66 runs while Sachin scored 2r i.e. 2 × 66 = runs.

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?

Solution:

Let Parmit's marbles be m

Given: 5 × Parmit's marbles + 7 = Irfan's marbles = 37

m + = 37

To isolate m, subtract on both sides.

5m + 7-7 = 37-7 which gives us m =

Divide by on both the sides.

m =

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

Solution:

Let Laxmi's age = m

Given: 3 × Laxmi's age + 4 = Laxmi's father age = 49

× m + =

To isolate m, subtract on both sides.

3m + 4 - 4 = 49 - 4 which gives =

Divide by on both the sides.

m =

(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?

Solution:

Let the number of fruit trees be 'f'.

Given: 3 × Fruit trees + 2 = Non-fruit trees =

× f + = 77

To isolate f, subtract on both sides.

3f + 2-2 = 77-2 giving us =

Divide by on both the sides.

Thus, f =

Thus, the number of fruit trees are 25.

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!

Instruction