Malachy, Sarah & Paul share some money in the ratio 1 : 9 : 3. In total, Malachy and Paul receive £52. How much does Sarah get?

Sarah gets £117

Step-by-step 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

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step-by-step explanation: