Simultaneous Equations

I like to think of maths as a means to practice clear thinking. There are those who criticise pure maths because it is not practical. People leave school and there are many mathematical processes that will never be used again. However there are lots of maths that is needed in day to day life. We need to get the right change, we need to buy the right amount of timber or sweets or dog food. We need to know how many minutes are in an hour, and we need to know about numbers when we drive at 30mph.

Maths is all around us but it is also a clear way of thinking. I have written about clear thought when talking about deal or no deal, and went on to talk about a system that is a little more complex - the Monty Hall problem. Well what if you sent two people to the chip shop and the first person bought three fish and two lots of chips and it costs £7.40 The second person two fish and one lot of chips and it costs £4.60 Now a third person wants fish and chips. How much is it going to cost them? If you don't know about simultaneous equations you have to phone the shop. If you do know about them the answer is in your grasp.

Let's put it mathematically and fish becomes f and chips becomes c. You end up with two equations: 3f + 2c = 7.4 and 2f + c = 4.6 The thing to do is learn to manipulate two sets of equations, and the question that you have to ask is what is the simplest way to end up with just fs or just cs? You can't simply add the equations together of take one from the other but if you do take the second from the first you get a third equation f + c = 2.8 Now take this from the second equation and you get f = 1.8 and you can now put this figure in any of the equations and you know the price of chips.

The actual costs of fish and chips doesn't matter. What does matter is that you know how to manipulate simultaneous equations so that you get your answer.

That sums it up