Topics › Ratio › Q124
Linked ratios · common units
P6 · Ratio · PSLE Maths
Question
Ali, Mei Ling and Raju collected 420 bookmarks altogether. The number of bookmarks Ali had : the number of bookmarks Mei Ling had = 2 : 3. The number of bookmarks Mei Ling had : the number of bookmarks Raju had = 4 : 5. How many bookmarks did Raju collect?
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Hint
Mei Ling appears in both ratios. First make Mei Ling's parts, 3 and 4, the same.
Show the answer and step-by-step explanation
Answer: Raju collected 180 bookmarks
- Find the link — There are two ratios. Mei Ling appears in both ratios, so she is the common person linking them.
- Make common units — The same Mei Ling must have the same number of parts. A common multiple of 3 and 4 is 12, so make Mei Ling 12 parts in both ratios.
- Draw blocks — Now combine the ratios: Ali : Mei Ling : Raju = 8 : 12 : 15. Draw the three amounts with equal-sized blocks.
- Find total units — The three children have 420 bookmarks altogether. In the block model, there are 8 + 12 + 15 = 35 units altogether.
- Find Raju — First find 1 unit: 420 ÷ 35 = 12. Raju has 15 units, so 15 × 12 = 180 bookmarks. 📌 Key idea: for linked ratios, make the common person's units the same first, then use the total to find 1 unit.
Method: For linked ratios, find the common person first. Make the common person's parts the same in both ratios, then combine them into A : B : C. Use the total to find 1 unit.
Practice: 3 similar questions
- Ali, Mei Ling and Raju have 372 game cards altogether. Ali : Mei Ling = 3 : 5 and Mei Ling : Raju = 2 : 3. How many game cards does Raju have?
Answer
180 game cards — Ali : Mei Ling = 3 : 5 = 6 : 10. Mei Ling : Raju = 2 : 3 = 10 : 15. So Ali : Mei Ling : Raju = 6 : 10 : 15. Total units = 31. 1 unit = 372 ÷ 31 = 12. Raju = 15 × 12 = 180 cards.
- At a school funfair, Siti, Raju and Mei Ling sold 380 muffins altogether. Siti : Raju = 5 : 6 and Raju : Mei Ling = 3 : 4. How many muffins did Mei Ling sell?
Answer
160 muffins — Siti : Raju = 5 : 6. Raju : Mei Ling = 3 : 4 = 6 : 8. So Siti : Raju : Mei Ling = 5 : 6 : 8. Total units = 19. 1 unit = 380 ÷ 19 = 20. Mei Ling = 8 × 20 = 160 muffins.
- Ali, Mei Ling and Raju collected stickers. Ali : Mei Ling = 2 : 3 and Mei Ling : Raju = 4 : 5. Ali and Raju have 345 stickers altogether. How many stickers does Mei Ling have?
Answer
180 stickers — Ali : Mei Ling = 2 : 3 = 8 : 12. Mei Ling : Raju = 4 : 5 = 12 : 15. So Ali : Mei Ling : Raju = 8 : 12 : 15. Ali and Raju make 8 + 15 = 23 units. 23 units = 345, so 1 unit = 15. Mei Ling = 12 × 15 = 180 stickers.
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