Topics › Ratio › Q109
Ratio · three quantities
P6 · Ratio · PSLE Maths
Question
At a school funfair, Ali, Mei Ling and Raju collected money for charity. The amounts they collected were in the ratio 4 : 5 : 7. Mei Ling and Raju collected $96 more altogether than Ali. How much money did each of them collect?
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Hint
Draw the ratio 4 : 5 : 7 as three bars. Then compare Mei Ling and Raju's units altogether with Ali's units.
Show the answer and step-by-step explanation
Answer: Ali collected 48 $; Mei Ling collected 60 $; Raju collected 84 $
- Draw 3 bars — The ratio is 4 : 5 : 7. So draw Ali as 4 units, Mei Ling as 5 units and Raju as 7 units. Each unit has the same value.
- Compare sums — The question says Mei Ling and Raju altogether collected $96 more than Ali. Mei Ling + Raju is 5 + 7 = 12 units, while Ali is 4 units.
- Find the gap — Altogether they have 12 units, and Ali has 4 units. The difference is 12 − 4 = 8 units. These 8 units are $96.
- Find 1 unit — Since 8 units = $96, 1 unit = 96 ÷ 8 = $12.
- Find each — Now multiply each person's number of units by $12. Ali has 4 units, Mei Ling has 5 units and Raju has 7 units.
- Check — Check: Mei Ling and Raju collected $60 + $84 = $144 altogether. This is $96 more than Ali's $48, so it fits the question. 📌 Key idea: draw a unit bar model for the three quantities. When two quantities together are more than another, compare the difference in units first, then find 1 unit.
Method: Represent the three quantities using equal units. If the question gives how much the sum of two quantities is more than another quantity, first find the difference in units, then find the value of 1 unit.
Practice: 3 similar questions
- Siti, Raju and Kenji collected erasers in the ratio 2 : 3 : 5. They collected 120 erasers altogether. How many erasers did each of them collect?
Answer
24 个, 36 个, 60 个 — Total number of units = 2 + 3 + 5 = 10 units. 1 unit = 120 ÷ 10 = 12 erasers. Siti: 2 × 12 = 24; Raju: 3 × 12 = 36; Kenji: 5 × 12 = 60 erasers.
- At a canteen, the numbers of packets of apple juice, orange juice and Milo sold in a day were in the ratio 6 : 4 : 9. There were 45 more packets of Milo sold than orange juice. How many packets of each drink were sold?
Answer
54 包, 36 包, 81 包 — Milo has 9 − 4 = 5 units more than orange juice. 5 units = 45 packets, so 1 unit = 45 ÷ 5 = 9 packets. Apple juice: 6 × 9 = 54 packets; orange juice: 4 × 9 = 36 packets; Milo: 9 × 9 = 81 packets.
- Ali, Raju and Siti saved money in the ratio 3 : 5 : 8. Ali and Siti saved $108 more altogether than Raju. How much money did the three of them save altogether?
Answer
288 $ — Ali + Siti = 3 + 8 = 11 units. They have 11 − 5 = 6 units more than Raju, so 6 units = $108. 1 unit = 108 ÷ 6 = $18. Total number of units = 3 + 5 + 8 = 16 units. Altogether, they saved 16 × 18 = $288.
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