3. 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 Cost of apples ($) 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

4. 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 sugar 4 eggs 150 g self-raising flour 1 tsp vanilla essence RECIPE: 200 g butter 160 g sugar 4 eggs 150 g self-raising flour 1 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

6. 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

7. 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

9. The graph can be used to convert between UK pounds (£) and US dollars ($). 02040 6080 100 0 80 120 160 200 40 UK pounds (£) US dollars ($) a Use the graph to convert £70 to US dollars. £70 ≈ $116 b Use the graph to convert $60 to UK pounds. $60 ≈ £36