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Proportion

Question)
If I drive 10 miles, I burn 6 litres of petrol. If I drive 20 miles I burn 12 litres of petrol. How many miles can I drive with 50 litres?

Answer)
This is a directly proportional relationship so if I call distance D and litres L, D α L

1) D α L

2) D=kL where k is some constant

3) 10 = k x 6

4) k = 10/6

5) k = 5/3

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Now that you know what k is, put it in to see what D is when L = 50

1) D = kL

2) D = 5/3 x 50

3) D = 250/3

4) D is 831/3

So I can drive 831/3 miles on 50 litres of petrol

 

Types of proportion

Direct)        a α b; when one doubles so does the other  

                   a α b2; a is directly proportional to the square of b so when a doubles, b2 doubles, not b!

Inverse)    a α b-1 or a α 1/b; when a doubles, b halves

                 a α b-2 or a α 1/(b2); when a doubles, b2 halves

NB a α b-1 means that a = k/b

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