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Ratio · constant total

P6 · Ratio · PSLE Maths

Question

At a school carnival, Ali and Mei Ling had some game coupons. At first, the ratio of Ali's coupons to Mei Ling's coupons was 3 : 5. Then Mei Ling gave Ali 24 coupons. The ratio became 5 : 7. How many coupons did Ali have at first?

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Hint

The total is unchanged. Make the total number of units the same for both ratios, then see how many units Ali gained.

Show the answer and step-by-step explanation

Answer: Ali at first 216 coupons

  1. Look at total — Mei Ling gave 24 coupons to Ali, so the coupons only moved from one person to the other. The total number of coupons stays the same.
  2. Same total units — At first, there are 3 + 5 = 8 units. After, there are 5 + 7 = 12 units. Since the total is the same, make both totals 24 units.
  3. Draw bars — Draw each bar with the same total of 24 units. At first, 3 : 5 becomes 9 : 15. After, 5 : 7 becomes 10 : 14.
  4. Find 24 coupons — Ali increased from 9 units to 10 units, so he gained 1 unit. This 1 unit is the 24 coupons Mei Ling gave him.
  5. Find at first — Ali had 9 units at first. So Ali had 9 × 24 = 216 coupons at first. 📌 Key idea: when the total is unchanged, rewrite the ratios with the same total number of units, then use the change in units to find 1 unit.

Method: When the total is constant, use the LCM of the total ratio units to rewrite both ratios with the same total number of units. Then match the change in units to the amount transferred.

Practice: 3 similar questions

  1. Raju and Siti had some cards. At first, the ratio of Raju's cards to Siti's cards was 2 : 3. Then Siti gave Raju 15 cards, and the ratio became 7 : 8. How many cards did Raju have at first?
    Answer

    90 cards — At first, the total ratio units are 2 + 3 = 5. After, they are 7 + 8 = 15. Use 15 units as the common total. At first, Raju : Siti = 6 : 9. After, Raju : Siti = 7 : 8. Raju gained 1 unit, so 1 unit = 15 cards. Raju had 6 × 15 = 90 cards at first.

  2. In an arcade game, the ratio of red tokens to blue tokens was 4 : 7. After Siti changed 36 blue tokens into red tokens, the ratio of red tokens to blue tokens became 5 : 6. How many tokens were there in all?
    Answer

    396 tokens — At first, the total ratio units are 4 + 7 = 11. After, they are 5 + 6 = 11, so the total units are already the same. The red tokens increased from 4 units to 5 units, a gain of 1 unit. This 1 unit is 36 tokens, so 1 unit = 36 tokens. There were 11 × 36 = 396 tokens in all.

  3. Ali and Raju had some stickers. At first, the ratio of Ali's stickers to Raju's stickers was 3 : 7. Then Raju gave Ali 45 stickers, and the ratio became 2 : 3. How many stickers did Raju have at first?
    Answer

    315 stickers — At first, the total ratio units are 3 + 7 = 10. After, they are 2 + 3 = 5, so rewrite the after ratio using 10 units. After, Ali : Raju = 2 : 3 = 4 : 6. Ali increased from 3 units to 4 units, so he gained 1 unit. This 1 unit = 45 stickers. Raju had 7 units at first, so 7 × 45 = 315 stickers.

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