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.
Steps Involved in Solving 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.
These are the steps most commonly involved in solving word problems in mathematics.
Let us see how these steps are involved in solving a word problem in math in the following example.
How to Solve Word problems in Mathematics - Example
Question :
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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WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Trigonometry word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
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