Answer:
Sarah gets £117
Explanation:
∵ Malachy, Sarah & Paul share some money in the ratio 1: 9: 3
∵ In total, Malachy and Paul receive £52
→ Use the ratio of Malachy and Paul and their sum to find their shares
→ Malachy : Paul : Total
→ 1 : 3 : 4 ⇒ (1 + 3)
→ x : y : 52
→ By using cross multiplication
∵ x × 4 = 1 × 52
∴ 4x = 52
→ Divide both sides by 4
∴ x = 13
∵ y × 4 = 3 × 52
∴ 4y = 156
→ Divide both sides by 4
∴ y = 39
∵ x represents Malachy's share and y represents Paul's share
∴ Malachy gets £13 and Paul gets £39
Use the ratio between Sarah and Paul to find the share of Sarah (you can use the ratio between Sarah and Malachy both will give the same share)
→ Sarah : Paul
→ 9 : 3
→ z : 39
→ By using cross multiplication
∵ z × 3 = 9 × 39
∴ 3z = 351
→ Divide both sides by 3
∴ z = 117
∵ z represents Sarah's share
∴ Sarah gets £117