Most people know that algebra is an extremely powerful problem solving tool. Simple problems encountered in everyday life can be solved mentally using common sense. Algebra enables you to solve problems that would be almost impossible by mere inspection. In fact, without algebra modern technology could never have been developed. In this section we first discuss simple mathematical word problems and then increase their complexity; more complex problems would require algebra and these will be discussed in later sections.
What is your age?
The problem is very simple, but like all algebra exercises considered here, it contains an unknown which is your age, which is related to a known which is your friend's age. We shall next consider a more complicated problem.
An integer is chosen between 0 and 10
A common strategy for answering the above question would be to test every integer between 1 and 10 until the right answer is discovered. Such a strategy is only practical since the range of values is restricted, but what if integer could take values say between 1-1000? then you would need the mental power of Mr Spock from Star Trek or Raymond from the film "The Rain Man". However, in later sections we shall learn how algebra can be used to solve problems which are far more complicated than the above question, and without the mental mathematical prowess of Mr Spock or Raymond. Instead, you shall develop algebraic prowess which forms the basis of modern science and engineering.
Try the exercise below:
Can you explain why the webpage obtains the correct answer every time? could the webpage be reading your mind? or is there a more rational explanation? You are advised show your working out on paper, and when you have determined the rational explanation you have then "discovered" the basis of algebra. A more formal introduction to algebra will be given in the next section.