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Basic Mathematics for Economists - Rosser - Chapter 3

3 Introduction to algebra Construct algebraic expressions for economic concepts involving unknown values. Simplify and reformulate basic algebraic expressions. Solve single linear equations with one unknown variable. Use the summation sign . Perform basic mathematical operations on algebraic expressions that involve inequality signs. | 3 Introduction to algebra Learning objectives After completing this chapter students should be able to Construct algebraic expressions for economic concepts involving unknown values. Simplify and reformulate basic algebraic expressions. Solve single linear equations with one unknown variable. Use the summation sign S. Perform basic mathematical operations on algebraic expressions that involve inequality signs. 3.1 Representation Algebra is basically a system of shorthand. Symbols are used to represent concepts and variables that are capable of taking different values. For example suppose that a biscuit manufacturer uses the following ingredients for each packet of biscuits produced 0.2 kg of flour 0.05 kg of sugar and 0.1 kg of butter. One way that we could specify the total amount of flour used is 0.2 kg times the number of packets of biscuits produced . However it is much simpler if we let the letter q represent the number of packets of biscuits produced. The amount of flour required in kilograms will then be 0.2 times q which we write as 0.2q. Thus we can also say amount of sugar required 0.05q kilograms amount of butter required 0.1q kilograms Sometimes an algebraic expression will have several terms in it with different algebraic symbols representing the unknown quantities of different variables. Consider the total expenditure on inputs by the firm in the example above. Let the price in per kilogram of flour be denoted by the letter a. The total cost of the amount of flour the firm uses will therefore be 0.2q times a written as 0.2qa. If the price per kilogram of sugar is denoted by the letter b and the price per kilogram of butter is c then the total expenditure in on inputs for biscuit production will be 0.2qa 0.05qb 0.1qc 1993 2003 Mike Rosser When two algebraic symbols are multiplied together it does not matter in which order they are written e.g. xy yx. This of course is the same rule that applies when multiplying numbers. For example 5 x 7 7 x 5 Any .