Translating word problem into simple equation

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 

Word problem into equation

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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