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Ratio · unchanged total and common parts
P6 · Ratio · PSLE Maths
Question
Mei Ling and Raju had some school funfair coupons in the ratio 7 : 5. Raju then gave 48 coupons to Mei Ling. After that, the ratio of Mei Ling's coupons to Raju's coupons became 5 : 3. How many coupons did Mei Ling have at first?
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Hint
Raju only gave coupons to Mei Ling, so the total number of coupons did not change. Make the total parts before and after the same.
Show the answer and step-by-step explanation
Answer: Mei Ling at first 672 coupons
- Find invariant — Raju gave 48 coupons to Mei Ling. The coupons only moved from one person to the other. So the total number is unchanged.
- Common parts — The total parts are 12 at first and 8 after. Use the LCM, 24, to make the total parts the same.
- Compare Raju — Look at Raju: he had 10 shares at first and 9 shares after. He lost 1 share, which is exactly the 48 coupons he gave to Mei Ling.
- Find first amount — Mei Ling had 14 shares at first. So Mei Ling had 14 × 48 = 672 coupons at first.
- Check — Check: Raju had 10 × 48 = 480 coupons at first. After giving 48 coupons, Raju had 432 and Mei Ling had 720. 720 : 432 = 5 : 3. 📌 Key idea: find the invariant first. When the total is unchanged, make the total parts the same, then match the change in parts to the given amount.
Method: First find the invariant: here, the total is unchanged. Make the total parts of the two ratios the same using the LCM, then compare one person's change to find 1 common part.
Practice: 3 similar questions
- Ali and Siti had some stickers in the ratio 4 : 3. After Siti gave Ali 20 stickers, the ratio of Ali's stickers to Siti's stickers became 3 : 2. How many stickers did Ali have at first?
Answer
400 stickers — At first, 4 : 3 has 7 total parts. After, 3 : 2 has 5 total parts. The LCM is 35. At first = 20 : 15, after = 21 : 14. Siti changed from 15 parts to 14 parts, a decrease of 1 part. 1 part = 20 stickers. Ali had 20 × 20 = 400 stickers at first.
- Mei Ling and her brother had savings in the ratio 5 : 4. Mei Ling spent $42 on a school bag, while her brother's savings did not change. After that, the ratio of Mei Ling's savings to her brother's savings became 2 : 3. How much money did Mei Ling have at first?
Answer
90 $ — Her brother's money is unchanged. He is 4 parts at first and 3 parts after; make these 12 parts. At first, 5 : 4 = 15 : 12. After, 2 : 3 = 8 : 12. Mei Ling decreased by 15 − 8 = 7 parts. These 7 parts are $42, so 1 part = $6. Mei Ling had 15 × $6 = $90 at first.
- Raju and Siti shared some game tokens in the ratio 7 : 5. After Raju gave some tokens to Siti, the ratio of Raju's tokens to Siti's tokens became 4 : 5. Siti had 120 more tokens than at first. How many tokens did Raju have at first?
Answer
504 tokens — At first, 7 : 5 has 12 total parts. After, 4 : 5 has 9 total parts. The LCM is 36. At first = 21 : 15, after = 16 : 20. Siti changed from 15 parts to 20 parts, an increase of 5 parts. 5 parts = 120 tokens, so 1 part = 24 tokens. Raju had 21 × 24 = 504 tokens at first.
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