3 ⋅6 Forming and applying algebraic formulae in solving real life problems
In our daily business we face the realistic problems in different time and in different
ways. These problems are described linguistically. In this section, we shall discuss
the formation of algebraic formulae and their applications in solving different
problems of real surroundings which are described linguistically. As a result of this
discussion the students on the one hand, will get the conception about the application
of mathematics in real surroundings, on the other hand, they will be eager to learn
mathematics for their understanding of the involvement of mathematics with their
surroundings.
Methods of solving the problems :
(a) At first the problem will have to be observed carefully and to read attentively
and then to identify which are unknown and which are to be determined.
(b) One of the unknown quantities is to be denoted with any variable (say x).
Then realising the problem well, express other unknown quantities in terms of
the same variable (x).
(c) The problem will have to be splitted into small parts and express them by
algebraic expressions.
(d) Using the given conditions, the small parts together are to be expressed by an equation.
(e) The value of the unknown quantity x is to be found by solving the equation.
Different formulae are used in solving the problems based on real life. The formulae
are mentioned below :
(1) Related to Payable or Attainable :
Payable or attainable, A Tk.qn
where, q = amount of money payable or attainable per person,
n = number of person.
(2) Related to Time and Work :
If some persons perform a work,
Amount of work done, W qnx
where, q = portion of a work performed by every one in unit of time.
n = number of performing of work
x = total time of doing work
(^) W portion of a work done by n persons in time x.
(3) Related to Time and Distance :
Distance at a definite time, d vt.