Applications Of Linear Equations To Practical Problems

Applications Of Linear Equations

In this section, we sill study formulation and solution of some practical problems. These problems involve relations among unknown quantities (variables) and known quantities (numbers) and are often stated in words. That is why we often refer to these problems as word problems. A word problem is first translated in the form of an equation containing unknown quantities (variables) and known quantities (numbers or constants) and then we solve it by using any one of the methods discussed in the earlier section. The procedure to translate a word problem in the form of an equation is known as the formulation of the problem. Thus, the process of solving a word problem consists of two parts, namely, formulation and solution.

The following steps should be followed to solve a word problem :

Step I:   Read the problem carefully and note what is given and what is required.

Step II:  Denote the unknown quantity by some letters, say x, y, z etc.

Step III: Translate the statements of the problem into mathematical statements.

Step IV: Using the condition(s) given in the problem, form the equation.

Step V : Solve the equation for the unknown.

Step VI: Check whether the solution satisfies the equation.

Process for Working Story/Word Problems

1. Read the problem.
2. Read the problem again.  However, the point of these first two steps is that you must read the problem. This step is the MOST important step, but it is also the step that most people don’t do properly. You need to read the problem very carefully and as many times as it takes.  You are only done with this step when you have completely understood what the problem is asking you to do.  This includes identifying all the given information and identifying what you being asked to find. Again, it can’t be stressed enough that you’ve got to carefully read the problem.  Sometimes a single word can completely change how the problem is worked.  If you just skim the problem you may well miss that very important word. Represent one of the unknown quantities with a variable and try to relate all the other unknown quantities (if there are any of course) to this variable.
3.  If applicable, sketch a figure illustrating the situation.  This may seem like a silly step, but it can be incredibly helpful with the next step on occasion.
4. Form an equation that will relate known quantities to the unknown quantities.  To do this make use of known formulas and often the figure sketched in the previous step can be used to determine the equation.
5. Solve the equation formed in the previous step and write down the answer to all the questions.  It is important to answer all the questions that you were asked.  Often you will be asked for several quantities in the answer and the equation will only give one of them.

THINGS TO REMEMBER

1.       Consecutive integers can be assumed as x, x + 1, x + 2, .......So on

2.       Perimeter of rectangle = 2(l + b) where l = length, b = breadth

3.       Perimeter of a quadrilateral = sum of 4 sides.

4.       Perimeter of a triangle = sum of lengths of 3 sides

5.       Perimeter of an equilateral triangle = 3 × side.

6.       Sum of four angles of a quadrilateral = 360⁰

7.       Sum of three angles of a triangle = 180⁰

8.       If sum of two angles = 90⁰, then they are called Complementary angles.

9.       If sum of two angles = 180⁰, then they are called Supplementary angles.

10.     Linear pair = 180⁰

11.     Straight angle = 180⁰

12.     Complete angle = 360⁰

13.     Loss = C.P. – S.P.

14.     Gain = s.p. – c.p.

15.     perimetre of a square  = 4( l ).