ALGEBRA WORD PROBLEMS

In this section, you will learn how to solve algebra word problems step by step.

Solving Algebra Word Problems - Steps

Step 1 :

Read the question twice and understand the information clearly. Because, always it is very important to understand the information given in the question. 

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 in algebra will  not be a challenging one. 

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 of 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 Algebra. 

Let us see how the above explained steps work in solving word problem in algebra.   

Question :

The denominator of a fraction exceeds the numerator by 5. If 3 be added to both, the fraction becomes 3/4. Find the fraction. 

Answer :

Step 1 :

In this problem, the denominator of the fraction is linked to the value in the numerator. 

That is, the denominator of a fraction exceeds the numerator by 5

Once we get the value of the numerator, easily we can get the value of the denominator and find the required fraction. 

Step 2 : 

Let x be the numerator.

Then, the denominator of the fraction is (x + 5). 

Therefore, the required fraction is 

=  x / (x + 5) -----(1)

Step 3 : 

It is given that if 3 be added to both, the fraction becomes 3/4. 

Then, we have

(x + 3) / (x + 5 + 3)  =  3 / 4

Simplify and solve fore x.

(x + 3) / (x + 8)  =  3/4

4(x + 3)  =  3(x + 8)

4x + 12  =  3x + 24

x  =  12

Step 4 : 

Substitute 12 for x in (1)

(1)----->  x / (x + 5)  =  12 / (12 + 5)

x / (x + 5)  =  12 / 17

So, the required fraction is 12 / 17. 

Topic Wise Word Problems in Algebra

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Word problems on simple equations 

Word problems on linear equations

Word problems on quadratic equations

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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 fractions

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