HOW TO SOLVE WORD PROBLEMS IN MATHEMATICS

The techniques and methods we apply to solve word problems in math will vary from problem to problem.

The techniques and methods we apply to solve a word problem in a particular topic in math will not work for another word problem found in some other topic.

For example, the methods we apply to solve the word problems in algebra will not work for the word problems in trigonometry.

Because, in algebra, we will solve most of the problems without any diagram. But, in trigonometry, for each word problem, we have to draw a diagram. Without diagram, always it is bit difficult to solve word problems in trigonometry. 

Even though we have different techniques to solve word problems in different topics of math, let us see the steps which are most commonly used.

The following steps would be useful to solve word problems in Mathematics. 

Step 1 :

Understanding the question is more important than any other thing. That is, always it is very important to understand the information given in the question rather than solving.

Step 2 :

If it is possible, we have to split the given information. Because, when we split the given information in to parts, we can understand them easily.

Step 3 :

Once we understand the given information clearly, solving the word problem would not be a challenging work. 

Step 4 :

When we try to solve the word problems, we have to introduce "x" or "y" or some other alphabet for unknown value (=answer for our question). Finally we have to get value for the alphabet which was introduced for the unknown value.

Step 5 :

If it is required, we have to draw picture for the given information. Drawing picture for the given information will give us a clear understanding about the question.

Step 6 :

Using the alphabet introduced for unknown value, we have to translate the English statement (information) given in the question as mathematical equation.

In translation, we have to translate  the following English words as the corresponding mathematical symbols.

                                  of ----> x (multiplication)

am, is, are, was, were, will be, would be ----> = (equal)

Step 7 :

Once we have translated the English Statement (information) given in the question as mathematical equation correctly, 90% of the work will be over. The remaining 10% is just getting the answer. That is solving for the unknown.

Example :

The age of a man is three times  the sum of the ages of his two sons and 5 years hence his age will be double the sum of their ages. Find the present age of the man.

Answer : 

Step 1 :

Let us understand the given information. There are two information given in the question. 

1. The age of a man is three times the sum of the ages of his two sons. (At present)

2. After 5 years, his age would be double the sum of their ages. (After 5 years)

Step 2 :

Target of the question :

Present age of the man = ?

Step 3 :

Introduce required variables for the information given in the question. 

Let x be the present age of the man.

Let y be the sum of present ages of two sons.

Clearly, the value of x to be found.

Because that is the target of the question.

Step 4 :

Translate the given information as mathematical equation using x and y. 

First information :  

The age of a man is three times the sum of the ages of his two sons.

Translation :

The Age of a man ----> x

is ----> =

Three times sum of the ages of his two sons ----> 3y 

Equation related to the first information using x and y is

x = 3y ----(1)

Second Information :

After 5 years, his age would be double the sum of their ages.

Translation :

Age of the man after 5 years ----> (x + 5)

Sum of the ages of his two sons after 5 years is

y + 5 + 5 = y + 10

(Because there are two sons, 5 is added twice)

Double the sum of ages of two sons ----> 2(y + 10)

would be ----> =

Equations related to the second information using x and y is

x + 5 = 2(y + 10) ----(2)

Step 5 :

Solve equations (1) & (2). 

From (1), substitute 3y for x in (2).

3y + 5 = 2(y + 10)

3y + 5 = 2y + 20

y = 15

Substitute 15 for y in (1).

x = 3(15)

x = 45

So, the present age of the man is 45 years. 

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