Exchange Rates & Best Buys (AQA GCSE Maths)
Revision Note
Author
MarkExpertise
Maths
Exchange Rates
Exchange rates are used when comparing and converting between different currencies. A good understanding of ratio and proportion is helpful for exchange rate conversion questions.
How do I simplify exchange rate questions?
- Using ratios is one of the easiest ways to compare, convert and simplify exchange rates
- STEP 1
Put exchange rates in ratio form (use more than one line if necessary) - STEP 2
Add lines for prices/costs - STEP 3
Use scale factors to complete lines - STEP 4
Pick out the answer
- STEP 1
Worked example
€1 (1 Euro) is worth $19.51 (Mexican Pesos).
₿1 (1 Bitcoin) is worth €20004.96 (Euro).
A vintage car costs $1000000 (Mexican Pesos).
What is the cost of the car in Bitcoin?
Convert $1000000 Mexican Peso to Euros.
Put the exchange rates in ratio form.
Euro : Mexican Peso = 1 : 19.51
Add a line for each rate.
Euro : Mexican Peso
Convert $1000000 Mexican Peso to Euros by dividing 1000000 by 19.51.
1000000 ÷ 19.51 = 51255.7662....
So $1000000 Mexican Peso = €51255.7662... Euro.
Convert €51255.7662... Euro to Bitcoin.
Put the exchange rates in ratio form.
Bitcoin : Euro = 1 : 20004.96
Add a line for each rate.
Bitcoin : Euro
Convert €51255.7662... Euro to Bitcoin by dividing 51255.7662... by 20004.96.
51255.7662... ÷ 20004.96 = 2.56215... Bitcoin
Round to a suitable degree of accuracy.
₿2.56 Bitcoin
Best Buys
You need to be able to determine, with clear reasoning, which deal being offered by shops is the best value for money.
How do I work out which deal is best?
- Find the price of 1 item (by dividing the number of items and total price by the same scale factor)
- e.g. if 3 tins cost £1.20 then 1 tin costs 40p (by dividing both quantities by 3)
- Compare the prices of 1 item from each shop / deal to see which is cheaper
- The cheaper deal is the better value for money
- e.g. 1 tin costs 40p from shop A and 45p from shop B
- 1 tin at shop A is cheaper than at shop B
- therefore shop A is the better value for money
- For more complicated deals, write down each line of working clearly
Worked example
Two deals for buying caps are given below:
3 caps for £22.50 from Baseball World
5 caps for £36 from Head Hut
At which shop are the caps better value?
You must show your working.
Find the cost of 1 cap from Baseball World (by dividing £22.50 by 3)
22.50 ÷ 3 = £7.50 for 1 cap from Baseball World
Find the cost of 1 cap from Head Hut (by dividing 36 by 5)
36 ÷ 5 = £7.20 for 1 cap from Head Hut
Compare the price of 1 cap from each shop to see which is cheapest
£7.20 is cheaper than £7.50
Write down, with reason, the shop with better value
1 cap from Head Hut costs £7.20 and 1 cap from Baseball World costs £7.50
£7.20 is cheaper than £7.50 so Head Hut is better value
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