Q.1 Write the following statements in the form of equations

(i) The sum of y and 10 is 27

Solution: According to the question,

We have y and 10 as two algebraic terms and their sum is 27

∴ Equation is Y + 10 = 27

(ii) The difference of 6 times a number and 11 is 55

Solution:

This statement has two parts,

Let the required number be x

∴ 6 times of the number be 6x

According to question , difference of 6 times a number and 11 is 55

6x -11 =55

Thus , required equation is 6x -11 =55

(iii) The sum of numbers p and 8 is 15 or p added to 8 gives 15

Solution: We have two numbers p and 8 when it added gives sum as 15

So, required equation p + 8 = 15

Q.2 There are 48 students in a class. If the number of girls is one-third the number of boys, form an equation to find the number of boys.

Solution:

Given :

Total no . of student(boys+girls) in the class =48

The number of girls is one-third the number of boys. So, we have to form an equation that finds the number of boys in the class

Let the no. of boys in the class be x

∴ No . of girls (which is one-third the number of boys) be \frac{1}{3} x.

Thus, the required equation be x + \frac{1}{3} x = 48 students

Q.3 Length of a rectangle is 6 m less than twice its breadth . The perimeter of the rectangle is 240 m.

Solution:

Let the breadth of the rectangle be x m

If length is 6 m less than twice the breadth i.e length = 2×breadth – 6

∴ The length of the rectangle be 2x – 6

Since the perimeter of the rectangle is 240 m .We know ,

Perimeter of rectangle = 2(L + B)

240= 2(2x-6 + x)

240=2(x -6 )

240=2x-12

So, required equation be 2x -12 = 240

Q.4 In an isosceles triangle, the vertex angle is thrice of either the base angle.

Solution: In order to solve this, you must be familiar with the Vertex angle and Base angle .

You can see vertex and base angle of a triangle in the given figure

According to the question, the vertex angle of the triangle is thrice of either the base angle.

Let the base angle of the triangle be x

∴ The vertex angle of the triangle be 3x

We know, the sum of three angles of the triangle =180º.In the given triangle, we have two equal base angles and a vertex angle

x + x +3x =180º

5x =180º

So, the required equation 5x= 180º where x is the vertex angle

Q.5 Vaibhav’s father’s age is 4 years more than three times Vaibhav’s age . Vaibhav’s Father is 43 years old.

Solution:

Let the Vaibhav’s age be x

Since Vaibhav’s father is 4 years more than three times Vaibhav’s age.

Three times Vaibhav age be 3x

∴ Vaibhav father’s age = 3×vaibhav age + 4

Vaibhav father’s age = 3x + 4

In the present time, Vaibhav father is 43 years old

So, required equation be 3x + 4 = 43

Q.6 Rahul scored twice as many runs as Gautam. The sum of their runs is 5 less than a double century.

Solution:

Let the total run scored by Gautam be x

∴ Run scored by Rahul = 2x

According to the problem, the sum of their runs is 5 less than a double century.

Double century means 200 runs, but sum Rahul and Gautam runs is 5 less than the double century i.e 200-5= 195

So, required equation be x + 2x = 195

Q.7 The sum of two consecutive numbers is 51

Solution:

Consecutive number = Numbers follow each other continuously without breaking the pattern like 1,2,3,4, etc

Let the two consecutive numbers are x, x+1.Since their sum is 51

∴ Required equation be x + x+ 1 = 51

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