In this section, we will study formulation and solution of some practical problems. These problems involve relations among unkown 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.
Example
A number is such that it is as much greater than 84 as it is less than 108. Find it.
Let the number be x. Then, the number is greater than 84 by x — 84 and it is less than 108 by 108 —x.
\( x-84 =108- x \) \( x+x = 108+84 \) \( 2x = 192 \) \( 2x/2- 192/2 \) \( = x = 96 \)