Mathematics Standard • Year 12 • Ratios and rates • Lesson 2

Ratios, Mastery Challenge

Work backwards from a single share, handle three-part ratios, and combine two ratios that share a common term.

Master · Mastery Challenge

1. Working backwards

You are given one share, not the total. 3 marks each

Q1.1 An amount is divided in the ratio 4:7. The SMALLER share is $180. Find the larger share and the total.

Q1.2 Three people share an amount in the ratio 2:3:5. The largest share is $60 more than the smallest. Find all three shares and the total.

Stuck? Ask which number of PARTS the given amount corresponds to, before dividing anything.

2. Three-part ratios

3 marks

Q2.1 A fertiliser blend mixes three ingredients in the ratio 1:2:4 and a batch weighs 35 kg. Find the mass of each ingredient.

3. Combining two ratios

4 marks

Q3.1 For three quantities a, b and c, a:b = 3:4 and b:c = 2:5. Find a:b:c in simplest form.

Stuck? The term b appears in both ratios. Scale each ratio so that b is the same number in both.

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Answers, Do not peek before attempting

Q1.1, Working back from the smaller share

The smaller share is 4 parts, so one part = 180 ÷ 4 = $45. Larger = 7 × 45 = $315, total = 11 × 45 = $495. Check: 180 + 315 = 495.

Q1.2, A difference between shares

Largest minus smallest = 5 − 2 = 3 parts = $60, so one part = $20. Shares $40, $60 and $100, total $200. Check: 100 − 40 = 60 and 40 + 60 + 100 = 200.

Q2.1, Three-part blend

parts = 1 + 2 + 4 = 7, one part = 35 ÷ 7 = 5 kg. Masses 5 kg, 10 kg and 20 kg. Check: 5 + 10 + 20 = 35.

Q3.1, Linking two ratios

Scale so b matches: 3:4 = 6:8 and 2:5 = 8:20. So a:b:c = 6:8:20 = 3:4:10. Check: a:b = 3:4 and b:c = 4:10 = 2:5.