HOW TO SOLVE WORD PROBLEMS USING SIMULTANEOUS EQUATIONS

About the topic "How to solve word problems using simultaneous equations"

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

How to solve word problems using simultaneous equations?

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

The techniques and methods we apply to solve a particular word problem using simultaneous equations  will not work for another word problem in the topic "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 using simultaneous equations"

Steps involved in solving word problems using simultaneous equations

To get answer for the question "How to solve word problems using simultaneous 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 would not be a challenging work. 

Step4:

When we try to solve the word problems using simultaneous equations, 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 word problems using simultaneous equations".

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

Problem:

A number consists of three digits of which the middle one is zero  and the sum of the other digits is 9. The number formed by interchanging the first and third digits is more than the original number by 297.Find the number. 

Solution:

Step 1 :

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

1. A number consists  of three digits of which the middle one is zero.

2. Sum of the digit in 100's place and 1's place is 9.

3. The number formed by interchanging the first and third digits is more than the original number by 297.

Step 2 :

Target of the question: What is that three digit number?

Step 3 :

Let "x0y" be the required three digit number. (As per the given information, middle digit is zero)

Step 4 :

In the three digit number "x0y", sum of the digit in 100's place and 1's place is 9.

That is   x + y = 9 --------> (1)

Step 5 :

The number formed by interchanging the first digit and third digit in "x0y" is "y0x"

Any three digit number can be written as given below.

526 = 100x5 + 10x2 + 1x6

In the same way, we can write "x0y"  and "y0x" as given below.

x0y = 100x(x) + 10x(0) + 1x(y) = 100x + y 

y0x = 100x(y) + 10x(0) + 1x(x) = 100y + x

Step 6 :

For example, we know that 797 is more than 500 by 297. 

If we want to balance 500 and 797, it has to be done as given below. 

That is,  500 + 297  =  797

Step 7 :

In our problem we have, "The number formed by interchanging the first and third digits is more than the original number by 297"

That is, "y0x" is more than "x0y" by 297.

If we want to balance "x0y" and "y0x", it has to be done as given below. 

That is,    x0y + 297 =  y0x

                100x + y + 297 = 100y + x

                 99x - 99y = -297

Divide by 99 on both the sides

                     x - y  =  -3  ----------(2)

Already we know that    x + y  =  9 -----------(1)


Step 8 :

By solving equations (1) & (2), we get x = 3 & y = 6

Therefore    x0y  =  306

Hence the required three digit number is 306

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 using simultaneous 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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