CHAPTER : 9 WORD PROBLEMS
9.1 Definition and Solving Techniques
Word problems must first be translated into mathematical language of equations which are then solved by mathematical methods. The result obtained must then be interpreted into the original language of the question.
First identify what you are asked for. Usually the last sentence tells you this.
Underline the valuable information. Choose proper letters to represent the unknown quantities. Write down exactly what they represent. Draw a picture or prepare a table if necessary.
Set up the equations with the given information.
Solve these equations or work out the necessary computations.
Check your answers and interpret them in terms of the original question
Be sure that you are working in the same units. Make sure that any error in computation or any mistake in setting up the equations does not give you an absurd answer. Note the ’key-words’ or ’key phrases’ of the problem carefully because they are the real "path finders."
A) Number Problems:
Note: If x is taken as the first number then,
The consecutive natural numbers would be x, x +1, x +2, . . .
The consecutive even (or odd) natural numbers would be x, x +2, x +4, . . .
Three consecutive natural numbers can also be written as x -1, x, x +1
Three consecutive even (or odd) natural number would be x -2, x, x +2
Example When 7 times a number is increased by 10, the result is 31. Find the number.
"Find the number" is what you have been asked to do.
Taking ’ x ’ for this number, we get the equation 7 x + 10 = 31
[Note: The key phrase " 7 times a number is increased by 10 " is translated as = 7 times the number is increased by 10 = 7 (x) + 10 and the result is 31 is translated as = 31]
\ 7 x = 31- 10 . . . ( on transposing)
\ 7 x = 21
\ x = 3
So the number is 3.
Definition and Solving Techniques
Use of Simultaneous Linear Equations