Many of you have come across problem which look more like English comprehension problem than mathematics riddle. Looks can indeed be deceptive. They usually come in the chapters of “Linear programing“, Application of derivative “,”application of differential equations.” etc. In some cases the problems may come from general topic such as function and relations, vector and 3D.
Here we are not considering problems from permutation and combination and Probability, coordinate geometry etc. because there are no other ways to represent these problems but by words. Let’s look at how to proceed with word problems and how to work through their solutions.
Look for the key words
Words such as “slope”, ”tangents”, ”rate” etc. give you a clue that they essentially mean dy/dx or dp/dt etc. essentially ratio of change of one quantity with respect to another. It can also mean the rate of change of a quantity w.r.t. time (in case of rate). Translate the problem into mathematical language. For example if the question says “slope of tangent at a point is twice the y coordinate of line point”. change it to dy/dx=2y.
Similarly translate every relevant sentence to mathematics and voila, you got the problem in the language, you are comfortable with i.e. mathematics.
Look for the objective of the problem
Read the problem carefully and find what you have to answer. If you have to calculate the no of pens a company has to produce give it a name, say x. Remember that whatever you have to calculate or find are variable /unknown. Your every effort should go towards getting as much information as possible about the unknown variable.
Look for any constraints
Constraints are conditions that put limitation on variables. More constraints are good things because they limit the scope of the variable. For example if a problem says X ÎN, you have to only consider natural number and not worry about rational, irrational, null, negative integers etc. This small condition limited the scope of your variable to just the natural number.
To summarize, every problem will have the following
objective :what is to be found.
Coustraints: the boundary within which you have to work
Other information: Help provided to let you proceed.
Combine these there factors and frame the question in mathematics .if you can do this, 80% of your problem in solved .Now do some calculation and make it 100%.
~ Pankaj Priyadarshi