2.1 Finding a word formula
Instead of looking for a way to show the relationship between miles and kilometres in a word formula, the next activity asks you to find a word formula to help work out the value of one currency in another. This is very similar to the previous example, as the focus is again on how much of one quantity is represented by another. The activity takes you step-by-step through the process of writing your own word formula.
(Again, remember that drawing diagrams can help you to spot relationships and patterns)
Activity 5 Exchanging currencies
Suppose somebody is visiting Europe, and they want to exchange some money from pounds (£) into euros (€). One agency offered an exchange rate of £1.00 to €1.18 and did not make any additional charges.
- a.How many euros would you get for £5? How many euros would you get for £10?
Click on ‘reveal comment’ if you would like a hint to get going.
Try drawing yourself a diagram to help visualise what you have been asked to find.
a.For each pound, you would get €1.18.
So for two pounds, you get two lots of €1.18, and for three pounds, three lots of €1.18 and so on.
Similarly, if £10 were exchanged, the person would get 10 lots of €1.18.
- b.Now, write down a word formula that can be used to convert pounds into euros.
b.To change pounds into euros, multiply the number of pounds by the exchange rate of €1.18. The word formula to represent this is:
You may also have thought of the more general word formula that will work with any exchange rate of:
- c.Check that your formula works by using it to convert £5 into euros.
c.Substituting 5 for ‘number of pounds’ gives:
This agrees with the answer in part (a) as expected, giving confidence that the word formula is correct.
These examples illustrate how a word formula can be used to summarise a mathematical process such as converting units of length or currencies. Once a formula has been derived, it can then be used in other situations, both for calculations by hand or by computer – for example, for currency transactions in a bank. You will be able to practise writing your own formulas next week.
Now let's look at using formulas in some more real-life examples.