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GCSEMathsOCRRevision Notes5. Ratio, Proportion & Rates of ChangeExchange Rates & Best BuysExchange Rates & Best Buys

Exchange Rates & Best Buys (OCR GCSE Maths)

Revision Note

Mark

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Mark

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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 
table row blank blank cell 1 space colon space 19.51 end cell row blank blank cell x space colon space 1000000 end cell end table

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 space colon space 20004.96 y space colon space 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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    Previous:Direct & Inverse ProportionNext:Interest & Depreciation
    Mark

    Author: Mark

    Expertise: Maths

    Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.