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Two quantities are in direct proportion if the graph of one quantity against the other quantity is a straight line through the origin.
So if one quantity doubles then the other quantity doubles.
Number of apples sold
Cos
t of
app
les
($)
1 The cost of five apples is $3.25. What is the cost of eight apples?
5 apples cost $3.25
1 apple cost $3.25 ÷ 5 =
8 apples cost $0.65 × 8 =
$0.65
$5.20
2 The recipe is for making cakes. The mixture will make two cakes. Helen wants to make seven cakes. Calculate the amount of each ingredient needed.
RECIPE:
200 g butter
160 g sugar4 eggs
150 g self-raising
flour1 tsp vanilla
essence
RECIPE:
200 g butter
160 g sugar4 eggs
150 g self-raising
flour1 tsp vanilla
essence
BUTTER: (200 ÷ 2) × 7 = 700 g
SUGAR: (160 ÷ 2) × 7 = 560g
EGGS: (4 ÷ 2) × 7 = 14 eggs
SELF-RAISING FLOUR: (150 ÷ 2) × 7 = 525 g
VANILLA ESSENCE: (1 ÷ 2) × 7 = 3.5 tsp
Two quantities are in inverse proportion if one quantity increases at the same rate as the other quantity decreases.So if one quantity doubles the other quantity halves.
1 It takes two men six hours to paint a fence. How long would it take three men to paint the
same fence?
2 men take 6 hours
1 man will take 2 × 6 hours =
3 men will take 12 ÷ 3 hours =
12 hours
4 hours
CHIRP
BIRD SEED
CHIRP
BIRD SEED
2 A box of bird seed lasts 5 birds 15 days. How long would the same packet of bird seed
last 30 birds?
5 birds for 15 days
1 bird for 15 × 5 days =
30 birds for 75 ÷ 30 days =
75 days
2.5 days
The graph can be used to convert between UK pounds (£) and US dollars ($).
0 20 40 60 80 1000
80
120
160
200
40
UK pounds (£)
US
dol
lars
($)
a Use the graph to convert £70 to US dollars. £70 ≈ $116
b Use the graph to convert $60 to UK pounds. $60 ≈ £36