Exchange Rates & Best Buys (OCR GCSE Maths)

Revision Note

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Author

Mark

Last updated

15 March 2023

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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

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
$\begin{array}{rcl} 1 : 19.51 \\ x : 1000000 \end{array}$

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
$1 : 20004.96 y : 51255.7662 . . . .$

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

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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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