# HOW TO SOLVE HARD WORD PROBLEMS IN ALGEBRA

## About the topic "How to solve hard word problems in algebra"

"How to solve hard word problems in algebra" is a big question having had by all the students who study algebra in both school level and college level math. Solving hard word problems in algebra is never being easy and always it is a challenging one for any student.

## How to solve hard word problems in algebra?

The answer  for the question "How to solve hard word problems in algebra ?" is purely depending upon the question that we have in the topic "Word Problems in Algebra". The techniques and methods we apply to solve word problems in algebra will vary from problem to problem.

The techniques and methods we apply to solve a particular word problem  will not work for another word problem in algebra.

In Algebra, we will solve most of the word problems in algebra 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 involved in "How to solve hard word problems in algebra"

## Steps involved in solving hard word problems in algebra

To get answer for the question "How to solve hard word problems in algebra ? ", we have to be knowing the following the steps explained.

Step1:

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.

Step2:

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.

Step3:

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

Step4:

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.

Step5:

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.

Step6:

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)

Step7:

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 "How to solve hard word problems in algebra".

Let us look at, how these steps are involved in solving the word problem given below. When you see the step by step explanation of the problem given below, you can clearly understand "How to solve hard word problems in algebra"

Problem:

A number between 10 and 100 is five times the sum of its digits. If 9 be added to it, the digits are reversed. Find the number.

Solution:

Step 1 :

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

1. A number between 10 and 100 is five times the sum of its digits.

2. If 9 be added to it, the digits are reversed.

Step 2 :

Target of the question: What is that  number?

Step 3 :

A number between 10  and 100 is clearly a two digit number.

Introduce required variables for the information given in the question.

Let "x" be the digit  at one's place.

Let "y" be the digit at ten's place.

So, the number is "xy" and we have to find "xy".

Step 4 :

Any two digit number can be written as given below.

56 = 10x5 + 1x6

(5 is at ten's place and 6 is at one's place)

In the same way we can write our two digit number "xy"

That is,    xy =  10x +  1y

Now, translate the given information as mathematical equation using "x" and "y".

Step 5 :

First information:

A number between 10 and 100 is five times the sum of its digits.

Translation:

A number between 10 and 100 ------->  "xy" = 10x + y

is --------> =   (equal)

Five times sum of the digits  --------> 5(x+y)

Equation related to the first information using "x" and "y" is

10x + y = 5(x+y)

10x + y = 5x + 5y

5x - 4y  = 0 ---------(1)

Step 6 :

Second Information:

If 9 be added to it, the digits are reversed.

Translation:

A number between 10 and 100 ------->  "xy"

When we add 9 to "xy", the digits are reversed. That is, "xy" will become "yx".

Equations related to the second information using "x" and "y" is

xy + 9  =  yx

10x + y + 9 = 10y + x

9x + 9 = 9y

Divide by 9 on both the sides.

x + 1 = y

(or)          y = x + 1  ---------(2)

Step 7 :

Solve equations (1) & (2) :

Plug y = x + 1  in equation (1) ===>  5x - 4(x+1) = 0

5x - 4x - 4 = 0

x = 4

Plug x = 4 in equation (2) ===> y = 4  + 1

y = 5

So,     xy  =  45

Therefore, the required number between 10 and 100 is 45.

Please click the below links to know "How to solve word problems in each of the given topics"

1. Solving Word Problems on Simple Equations

2. Solving Word Problems on Simultaneous Equations

3. Solving Word Problems on Quadratic Equations

4. Solving Word Problems on Permutations and Combinations

5. Solving Word Problems on HCF and LCM

7. Solving Word Problems on Time and Work

8. Solving Word Problems on Trains

9. Solving Word Problems on Time and Work.

10. Solving Word Problems on Ages.

11.Solving Word Problems on Ratio and Proportion

12.Solving Word Problems on Allegation and Mixtures.

13. Solving Word Problems on Percentage

14. Solving Word Problems on Profit and Loss

15. Solving Word Problems Partnership

16. Solving Word Problems on Simple Interest

17. Solving Word Problems on Compound Interest

18. Solving Word Problems on Calendar

19. Solving Word Problems on Clock

20. Solving Word Problems on Pipes and Cisterns

21. Solving Word Problems on Modular Arithmetic