Unit 2: Section 1 - Standard Form With Negative Indices Examples And Worksheets Page 7
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14Direct proportion
In mathematics, there are many ways to relate two quantities together. Here are a few examples.
Change of units: 1 mile � 1.609 km
Velocities: 30 miles travelled in 1 hour (30 miles/hour)
Gradients: 1 in 5
Scales: 1 : 50
Bureau de Change 1 mile 1.6 km
Equations: 3x � 5 � 16
Exchange rates: £1 � $1.60
Ratio: 4 : 5
y
Graphs
(two axes)
Densities: 13 g is the mass of 1 cm
(13 g/cm
)
3
3
x
Problem solving: 3.4 m of timber costs $6.80 ($2/m)
Two different ways of doing the same calculation are shown in Example 14.
Example 14
The committee that organised the Athens Olympics in 2004 recycled 108 tonnes of
paper, saving 1836 trees and cutting energy consumption by 442 800 kW.
Calculate the amount of energy saved by recycling one tonne of paper.
Method 1 ‘unitary method’
108 tonnes
save
442 800 kW
Remember
442 800
________
‘Per’ means divide. For
So
1 tonne
saves
kW 5 4100 kW
108
example, ‘miles per hour’
Method 2 ‘per method’
means miles divided by
Total energy saved
442 800
________________
________
Energy saved per tonne 5
5 4100 kW per tonne
5
hours, or miles/hour.
Total tonnage
108
Exercise XX
For Questions 1–6, find the exchange rate in the form £1 5 … .
1 £6 5 ¥1080
2 US$15 5 £9
3 Aus$62 5 £26
4 £7 5 US$13
5 NZ$22 5 £8
6 Can$54 5 £24
7 4 m of timber costs $33.60.
a What is the cost of 1 m?
b What is the cost of 9 m?
8 Three CDs cost $33.75.
a What is the cost of one CD?
b What is the cost of seven CDs?
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