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Primary 6 · Ratio · Question type 1.5

P6 Ratio: Constant Total Questions

When an amount moves from one side to the other, the total stays unchanged because nothing enters or leaves. This is a constant total problem: match the total units before and after.

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Primary 6, on the MOE Primary Mathematics syllabus.

In the Ratio chapter10 question types · see the chapter

The lesson · 1 minute 57 seconds

How do you solve P6 ratio questions with a constant total?

Watch: 24 marbles change hands and the total stays the same

Another worked example

A worked example

The number of marbles Chloe and Marcus had was in the ratio 7 : 3. Chloe then gave Marcus 24 marbles, and they had the same number each. How many marbles did Chloe have at first?

The working · Six lines

The step-by-step working

Written out in full, the way it should appear on paper.

  1. total = 7 + 3 = 10 units
  2. 10 units ÷ 2 = 5 units each
  3. 7 units - 5 units = 2 units
  4. 2 units = 24
  5. 1 unit = 24 ÷ 2 = 12
  6. 7 units = 7 × 12 = 84 marbles

Chloe had 84 marbles at first.

Practise · Modelled on top school exam questions

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Find the total stickers

Try solving it yourself before checking your answer and working.

The number of stickers in Album A to the number of stickers in Album B was in the ratio 5 : 3. 1/4 of the stickers in Album A were then moved to Album B. In the end Album B held 42 more stickers than Album A. How many stickers were there in the two albums altogether?

Show the step-by-step solution
  1. Album A : Album B = 5 : 3
  2. a quarter of Album A moves, so Album A must divide into quarters
  3. Album A reads 5, and it has to reach a multiple of 4: 5 × 4 = 20
  4. Album A : Album B = 5 : 3
  5. × 4 = 20 : 12
  6. before, 20 + 12 = 32 units
  7. the stickers only changed album, so the end counts the same 32 units
  8. stickers moved = 1/4 of 20 units = 5 units
  9. Album A in the end = 20 units - 5 units = 15 units
  10. Album B in the end = 12 units + 5 units = 17 units
  11. Album B - Album A = 17 units - 15 units = 2 units
  12. 2 units = 42
  13. 1 unit = 42 ÷ 2 = 21
  14. 32 units = 32 × 21 = 672 stickers

Ans: 672

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