HOW TO SOLVE WORD PROBLEMS IN QUADRATIC EQUATIONS

About the topic "How to solve word problems in quadratic equations"

"How to solve word problems in quadratic equations" is a big question having had by all the students who study math in all levels. For some students, solving word problems in quadratic equations is never being easy and always it is a challenging one.

How to solve word problems in quadratic equations ?

The answer  for the question "How to solve word problems in quadratic equations ?" is purely depending upon the question that we have in the topic "Quadratic Equations". The techniques and methods we apply to solve word problems in quadratic equations  will vary from problem to problem.

The techniques and methods we apply to solve a particular word problem in quadratic equations will not work for another word problem in the topic "Quadratic Equations" .

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 word problems in quadratic equations"

Steps involved in solving word problems in quadratic equations

To get answer for the question "How to solve word problems in quadratic equations ?", we have to be knowing the following 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 in quadratic equation would not be a challenging work. 

Step4:

When we try to solve the word problems in quadratic equations, we have to introduce "x" or some other alphabet for unknown value (=answer for our question) and form a quadratic equation with this "x". 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 quadratic equation 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 quadratic 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 word problems in quadratic equations".

Let us look at, how these steps are involved in solving the word problem given below.

Problem:

A piece of iron rod cost $ 60. If the rod was 2 meter shorter and each meter costs $ 1 more and the total cost  would remain unchanged. What is the length of the rod? 

Solution:

Step 1 :

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

1. A piece of iron rod costs $ 60.

2.  If the rod was 2 meter shorter and each meter costs $ 1 more

3 Total cost  would remain unchanged.

Step 2 :

Target of the question: What is the length of the rod?

Step 3 :

Let "x" be the length of the rod.

Clearly, we have to find the value of "x"

Step 4 :

If the rod is 2 meter shorter, length of the rod = (x-2)

Step 5 :

From the third information, we have the following statements.

Total cost of rod having length "x" meters =  $ 60

Total cost of rod having length "(x-2)" meters =  $ 60

Step 6 :

Cost of 1 meter of rod having length "x" meters

                                         = 60/x  ------------(1)

Cost of 1 meter of rod having length "(x-2)" meters

                                         = 60/(x-2) --------(2)

Step 7 :

From the second information, we can consider the following example.

That is, if the cost of 1 meter of  rod "x" is $10 , then the cost of 1 meter of rod "(x-2)" will be $11 

$10 &  $11 can be balanced as given below.

                                          10 + 1 = 11

(This is just for en example)

Step 8 :

If we apply the same logic for (1) & (2), we get 

                                    (60/x) + 1 = 60/(x-2)

                                     (60 + x)/x = 60/(x-2)

                                   (x+60)(x-2) = 60x

                             x²  + 58x - 120 = 60x

                                  x² - 2x - 120 = 0

                                  (x-12)(x+10) = 0

                         x - 12 = 0      or      x + 10 = 0

                            x = 12         or      x = - 10

x= -10 can not be accepted. Because length can never be negative.

Therefore   x  =  12

Hence the length of the rod is 12 meter.

After having seen the steps explained in the above word problem, we hope that the students would have received answer for the question "How to solve word problems in quadratic equations?"

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

6. Solving Word Problems on Numbers

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

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