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ReasoningAges 7-9

Balance scale puzzles

Use equal-weight reasoning to work out the mass of a single mystery box on a balanced scale. Review suitability for your learners before teaching.

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Age band:Ages 7-9Ages 10-12

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Worksheet StudioPractice pack · Ages 7-9

Balance scale puzzles

Take your time. Show your thinking.

  1. 1. 3 identical boxes and a 12 kg weight balance 42 kg altogether. What is the mass of 1 box?

    3 · 12 kg · 42 kg · 1 · Balance scale puzzles

  2. 2. 4 identical boxes and a 4 kg weight balance 44 kg altogether. What is the mass of 1 box?

    4 · 4 kg · 44 kg · 1 · Balance scale puzzles

  3. 3. 4 identical boxes and a 6 kg weight balance 50 kg altogether. What is the mass of 1 box?

    4 · 6 kg · 50 kg · 1 · Balance scale puzzles

  4. 4. 5 identical boxes and a 7 kg weight balance 72 kg altogether. What is the mass of 1 box?

    5 · 7 kg · 72 kg · 1 · Balance scale puzzles

  5. 5. 5 identical boxes and a 2 kg weight balance 72 kg altogether. What is the mass of 1 box?

    5 · 2 kg · 72 kg · 1 · Balance scale puzzles

  6. 6. 3 identical boxes and a 8 kg weight balance 50 kg altogether. What is the mass of 1 box?

    3 · 8 kg · 50 kg · 1 · Balance scale puzzles

  7. 7. 4 identical boxes and a 5 kg weight balance 25 kg altogether. What is the mass of 1 box?

    4 · 5 kg · 25 kg · 1 · Balance scale puzzles

  8. 8. 3 identical boxes and a 4 kg weight balance 43 kg altogether. What is the mass of 1 box?

    3 · 4 kg · 43 kg · 1 · Balance scale puzzles

  9. 9. 2 identical boxes and a 2 kg weight balance 24 kg altogether. What is the mass of 1 box?

    2 · 2 kg · 24 kg · 1 · Balance scale puzzles

  10. 10. 2 identical boxes and a 8 kg weight balance 28 kg altogether. What is the mass of 1 box?

    2 · 8 kg · 28 kg · 1 · Balance scale puzzles

  11. 11. 5 identical boxes and a 10 kg weight balance 60 kg altogether. What is the mass of 1 box?

    5 · 10 kg · 60 kg · 1 · Balance scale puzzles

  12. 12. 2 identical boxes and a 4 kg weight balance 30 kg altogether. What is the mass of 1 box?

    2 · 4 kg · 30 kg · 1 · Balance scale puzzles
12 questions · Seed 47 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 7-9

Balance scale puzzles

Answers and reasoning. Review before teaching.

  1. 1. 3 identical boxes and a 12 kg weight balance 42 kg altogether. What is the mass of 1 box?

    10 kg

    Subtract 12 kg from 42 kg to get 30 kg for 3 boxes. Divide by 3: 10 kg per box.

  2. 2. 4 identical boxes and a 4 kg weight balance 44 kg altogether. What is the mass of 1 box?

    10 kg

    Subtract 4 kg from 44 kg to get 40 kg for 4 boxes. Divide by 4: 10 kg per box.

  3. 3. 4 identical boxes and a 6 kg weight balance 50 kg altogether. What is the mass of 1 box?

    11 kg

    Subtract 6 kg from 50 kg to get 44 kg for 4 boxes. Divide by 4: 11 kg per box.

  4. 4. 5 identical boxes and a 7 kg weight balance 72 kg altogether. What is the mass of 1 box?

    13 kg

    Subtract 7 kg from 72 kg to get 65 kg for 5 boxes. Divide by 5: 13 kg per box.

  5. 5. 5 identical boxes and a 2 kg weight balance 72 kg altogether. What is the mass of 1 box?

    14 kg

    Subtract 2 kg from 72 kg to get 70 kg for 5 boxes. Divide by 5: 14 kg per box.

  6. 6. 3 identical boxes and a 8 kg weight balance 50 kg altogether. What is the mass of 1 box?

    14 kg

    Subtract 8 kg from 50 kg to get 42 kg for 3 boxes. Divide by 3: 14 kg per box.

  7. 7. 4 identical boxes and a 5 kg weight balance 25 kg altogether. What is the mass of 1 box?

    5 kg

    Subtract 5 kg from 25 kg to get 20 kg for 4 boxes. Divide by 4: 5 kg per box.

  8. 8. 3 identical boxes and a 4 kg weight balance 43 kg altogether. What is the mass of 1 box?

    13 kg

    Subtract 4 kg from 43 kg to get 39 kg for 3 boxes. Divide by 3: 13 kg per box.

  9. 9. 2 identical boxes and a 2 kg weight balance 24 kg altogether. What is the mass of 1 box?

    11 kg

    Subtract 2 kg from 24 kg to get 22 kg for 2 boxes. Divide by 2: 11 kg per box.

  10. 10. 2 identical boxes and a 8 kg weight balance 28 kg altogether. What is the mass of 1 box?

    10 kg

    Subtract 8 kg from 28 kg to get 20 kg for 2 boxes. Divide by 2: 10 kg per box.

  11. 11. 5 identical boxes and a 10 kg weight balance 60 kg altogether. What is the mass of 1 box?

    10 kg

    Subtract 10 kg from 60 kg to get 50 kg for 5 boxes. Divide by 5: 10 kg per box.

  12. 12. 2 identical boxes and a 4 kg weight balance 30 kg altogether. What is the mass of 1 box?

    13 kg

    Subtract 4 kg from 30 kg to get 26 kg for 2 boxes. Divide by 2: 13 kg per box.

12 questions · Seed 47 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 7-9

Balance scale puzzles

Take your time. Show your thinking.

  1. 1. 3 identical boxes and a 12 kg weight balance 42 kg altogether. What is the mass of 1 box?

    3 · 12 kg · 42 kg · 1 · Balance scale puzzles

  2. 2. 4 identical boxes and a 4 kg weight balance 44 kg altogether. What is the mass of 1 box?

    4 · 4 kg · 44 kg · 1 · Balance scale puzzles

  3. 3. 4 identical boxes and a 6 kg weight balance 50 kg altogether. What is the mass of 1 box?

    4 · 6 kg · 50 kg · 1 · Balance scale puzzles

  4. 4. 5 identical boxes and a 7 kg weight balance 72 kg altogether. What is the mass of 1 box?

    5 · 7 kg · 72 kg · 1 · Balance scale puzzles

  5. 5. 5 identical boxes and a 2 kg weight balance 72 kg altogether. What is the mass of 1 box?

    5 · 2 kg · 72 kg · 1 · Balance scale puzzles

  6. 6. 3 identical boxes and a 8 kg weight balance 50 kg altogether. What is the mass of 1 box?

    3 · 8 kg · 50 kg · 1 · Balance scale puzzles

  7. 7. 4 identical boxes and a 5 kg weight balance 25 kg altogether. What is the mass of 1 box?

    4 · 5 kg · 25 kg · 1 · Balance scale puzzles

  8. 8. 3 identical boxes and a 4 kg weight balance 43 kg altogether. What is the mass of 1 box?

    3 · 4 kg · 43 kg · 1 · Balance scale puzzles

  9. 9. 2 identical boxes and a 2 kg weight balance 24 kg altogether. What is the mass of 1 box?

    2 · 2 kg · 24 kg · 1 · Balance scale puzzles

  10. 10. 2 identical boxes and a 8 kg weight balance 28 kg altogether. What is the mass of 1 box?

    2 · 8 kg · 28 kg · 1 · Balance scale puzzles

  11. 11. 5 identical boxes and a 10 kg weight balance 60 kg altogether. What is the mass of 1 box?

    5 · 10 kg · 60 kg · 1 · Balance scale puzzles

  12. 12. 2 identical boxes and a 4 kg weight balance 30 kg altogether. What is the mass of 1 box?

    2 · 4 kg · 30 kg · 1 · Balance scale puzzles
12 questions · Seed 47 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 7-9

Balance scale puzzles

Answers and reasoning. Review before teaching.

  1. 1. 3 identical boxes and a 12 kg weight balance 42 kg altogether. What is the mass of 1 box?

    10 kg

    Subtract 12 kg from 42 kg to get 30 kg for 3 boxes. Divide by 3: 10 kg per box.

  2. 2. 4 identical boxes and a 4 kg weight balance 44 kg altogether. What is the mass of 1 box?

    10 kg

    Subtract 4 kg from 44 kg to get 40 kg for 4 boxes. Divide by 4: 10 kg per box.

  3. 3. 4 identical boxes and a 6 kg weight balance 50 kg altogether. What is the mass of 1 box?

    11 kg

    Subtract 6 kg from 50 kg to get 44 kg for 4 boxes. Divide by 4: 11 kg per box.

  4. 4. 5 identical boxes and a 7 kg weight balance 72 kg altogether. What is the mass of 1 box?

    13 kg

    Subtract 7 kg from 72 kg to get 65 kg for 5 boxes. Divide by 5: 13 kg per box.

  5. 5. 5 identical boxes and a 2 kg weight balance 72 kg altogether. What is the mass of 1 box?

    14 kg

    Subtract 2 kg from 72 kg to get 70 kg for 5 boxes. Divide by 5: 14 kg per box.

  6. 6. 3 identical boxes and a 8 kg weight balance 50 kg altogether. What is the mass of 1 box?

    14 kg

    Subtract 8 kg from 50 kg to get 42 kg for 3 boxes. Divide by 3: 14 kg per box.

  7. 7. 4 identical boxes and a 5 kg weight balance 25 kg altogether. What is the mass of 1 box?

    5 kg

    Subtract 5 kg from 25 kg to get 20 kg for 4 boxes. Divide by 4: 5 kg per box.

  8. 8. 3 identical boxes and a 4 kg weight balance 43 kg altogether. What is the mass of 1 box?

    13 kg

    Subtract 4 kg from 43 kg to get 39 kg for 3 boxes. Divide by 3: 13 kg per box.

  9. 9. 2 identical boxes and a 2 kg weight balance 24 kg altogether. What is the mass of 1 box?

    11 kg

    Subtract 2 kg from 24 kg to get 22 kg for 2 boxes. Divide by 2: 11 kg per box.

  10. 10. 2 identical boxes and a 8 kg weight balance 28 kg altogether. What is the mass of 1 box?

    10 kg

    Subtract 8 kg from 28 kg to get 20 kg for 2 boxes. Divide by 2: 10 kg per box.

  11. 11. 5 identical boxes and a 10 kg weight balance 60 kg altogether. What is the mass of 1 box?

    10 kg

    Subtract 10 kg from 60 kg to get 50 kg for 5 boxes. Divide by 5: 10 kg per box.

  12. 12. 2 identical boxes and a 4 kg weight balance 30 kg altogether. What is the mass of 1 box?

    13 kg

    Subtract 4 kg from 30 kg to get 26 kg for 2 boxes. Divide by 2: 13 kg per box.

12 questions · Seed 47 · Age guidance, not curriculum certification