Mathematics Problem Solving Questions And Answers

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

HCF and LCM word problems

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6