Ratio, Proportion and Rates — Solutions

Full worked solutions, with method and final answer for every part.

Question 1

(a)Total parts = 2+3+4 = 9. One part = 360 ÷ 9 = 40.

Shares = 2×40, 3×40, 4×40 = $80, $120, $160

Question 2

(a)Speed = distance ÷ time.

150 ÷ 2.5 = 60 km/h

Question 3

(a)Find the amount per person, then scale up: 300 ÷ 4 = 75 g per person.

75 × 7 = 525 g

Question 4

(a)Total parts = 8, so one part = 240 ÷ 8 = 30.

3 × 30 = $90, 5 × 30 = $150

Question 5

(a)Multiply map distance by the scale factor, then convert cm to m (÷100).

5 × 20 000 = 100 000 cm = 1000 m

Question 6

(a)Speed = distance ÷ time.

240 ÷ 3 = 80 km/h

Question 7

(a)Blue:white = 2:7, so blue = (2/7) × white amount.

(2/7) × 3.6 ≈ 1.03 litres

Question 8

(a)Divide both parts by their HCF (15).

45÷15 : 60÷15 = 3:4

Question 9

(a)Find the amount per person, then scale up: 450 ÷ 6 = 75 g per person.

75 × 10 = 750 g

Question 10

(a)Total parts = 10, one part = 40.

3×40=120, 7×40=280

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