This lesson submitted by amanda.bragg
Equations and inequalities: Mathematical models
Tom and Jane are friends. Tom picked up Jane's Physics test paper, but will not tell Jane what her marks are. He knows that Jane hates maths so he decided to tease her. Tom says: 'I have 2 marks more than you do and the sum of both our marks is equal to 14. How much did we get?'
Let's help Jane find out what her marks are. We have two unknowns, Tom's mark (which we shall call t) and Jane's mark (which we shall call j). Tom has 2 more marks than Jane. Therefore,
Also, both marks add up to 14. Therefore,
The two equations make up a set of linear (because the highest power is one) simultaneous equations, which we know how to solve! Substitute for t in the second equation to get:
So, we see that Tom scored 8 on his test and Jane scored 6.
This problem is an example of a simple mathematical model. We took a problem and we were able to write a set of equations that represented the problem mathematically. The solution of the equations then gave the solution to the problem.
Problem Solving Strategy
The purpose of this section is to teach you the skills that you need to be able to take a problem and formulate it mathematically in order to solve it. The general steps to follow are:
- Read ALL of the question !
- Find out what is requested.
- Use a variable(s) to denote the unknown quantity/quantities that has/have been requested e.g., x.
- Rewrite the information given in terms of the variable(s). That is, translate the words into algebraic expressions.
- Set up an equation or set of equations (i.e. a mathematical sentence or model) to solve the required variable.
- Solve the equation algebraically to find the result.
Application of Mathematical Modelling
EXERCISE 1: Mathematical Modelling: Two variables
Three rulers and two pens have a total cost of R 21,00. One ruler and one pen have a total cost of R 8,00. How much does a ruler costs on its own and how much does a pen cost on its own?
EXERCISE 2: Mathematical Modelling: One variable
A fruit shake costs R2,00 more than a chocolate milkshake. If three fruit shakes and 5 chocolate milkshakes cost R78,00, determine the individual prices.
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