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 7-9 Ages 10-12

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Worksheet StudioPractice pack · Ages 7-9

Balance scale puzzles

Take your time. Show your thinking.

1. 6 identical boxes and a 12 kg weight balance 96 kg altogether. What is the mass of 1 box?
6 · 12 kg · 96 kg · 1 · Balance scale puzzles
2. 5 identical boxes and a 2 kg weight balance 67 kg altogether. What is the mass of 1 box?
5 · 2 kg · 67 kg · 1 · Balance scale puzzles
3. 6 identical boxes and a 5 kg weight balance 53 kg altogether. What is the mass of 1 box?
6 · 5 kg · 53 kg · 1 · Balance scale puzzles
4. 5 identical boxes and a 6 kg weight balance 46 kg altogether. What is the mass of 1 box?
5 · 6 kg · 46 kg · 1 · Balance scale puzzles
5. 3 identical boxes and a 4 kg weight balance 25 kg altogether. What is the mass of 1 box?
3 · 4 kg · 25 kg · 1 · Balance scale puzzles
6. 3 identical boxes and a 1 kg weight balance 10 kg altogether. What is the mass of 1 box?
3 · 1 kg · 10 kg · 1 · Balance scale puzzles
7. 2 identical boxes and a 5 kg weight balance 27 kg altogether. What is the mass of 1 box?
2 · 5 kg · 27 kg · 1 · Balance scale puzzles
8. 4 identical boxes and a 4 kg weight balance 12 kg altogether. What is the mass of 1 box?
4 · 4 kg · 12 kg · 1 · Balance scale puzzles
9. 5 identical boxes and a 8 kg weight balance 38 kg altogether. What is the mass of 1 box?
5 · 8 kg · 38 kg · 1 · Balance scale puzzles
10. 2 identical boxes and a 9 kg weight balance 17 kg altogether. What is the mass of 1 box?
2 · 9 kg · 17 kg · 1 · Balance scale puzzles
11. 2 identical boxes and a 1 kg weight balance 29 kg altogether. What is the mass of 1 box?
2 · 1 kg · 29 kg · 1 · Balance scale puzzles
12. 4 identical boxes and a 9 kg weight balance 45 kg altogether. What is the mass of 1 box?
4 · 9 kg · 45 kg · 1 · Balance scale puzzles

12 questions · Seed 46 · 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. 6 identical boxes and a 12 kg weight balance 96 kg altogether. What is the mass of 1 box?
14 kg
Subtract 12 kg from 96 kg to get 84 kg for 6 boxes. Divide by 6: 14 kg per box.
2. 5 identical boxes and a 2 kg weight balance 67 kg altogether. What is the mass of 1 box?
13 kg
Subtract 2 kg from 67 kg to get 65 kg for 5 boxes. Divide by 5: 13 kg per box.
3. 6 identical boxes and a 5 kg weight balance 53 kg altogether. What is the mass of 1 box?
8 kg
Subtract 5 kg from 53 kg to get 48 kg for 6 boxes. Divide by 6: 8 kg per box.
4. 5 identical boxes and a 6 kg weight balance 46 kg altogether. What is the mass of 1 box?
8 kg
Subtract 6 kg from 46 kg to get 40 kg for 5 boxes. Divide by 5: 8 kg per box.
5. 3 identical boxes and a 4 kg weight balance 25 kg altogether. What is the mass of 1 box?
7 kg
Subtract 4 kg from 25 kg to get 21 kg for 3 boxes. Divide by 3: 7 kg per box.
6. 3 identical boxes and a 1 kg weight balance 10 kg altogether. What is the mass of 1 box?
3 kg
Subtract 1 kg from 10 kg to get 9 kg for 3 boxes. Divide by 3: 3 kg per box.
7. 2 identical boxes and a 5 kg weight balance 27 kg altogether. What is the mass of 1 box?
11 kg
Subtract 5 kg from 27 kg to get 22 kg for 2 boxes. Divide by 2: 11 kg per box.
8. 4 identical boxes and a 4 kg weight balance 12 kg altogether. What is the mass of 1 box?
2 kg
Subtract 4 kg from 12 kg to get 8 kg for 4 boxes. Divide by 4: 2 kg per box.
9. 5 identical boxes and a 8 kg weight balance 38 kg altogether. What is the mass of 1 box?
6 kg
Subtract 8 kg from 38 kg to get 30 kg for 5 boxes. Divide by 5: 6 kg per box.
10. 2 identical boxes and a 9 kg weight balance 17 kg altogether. What is the mass of 1 box?
4 kg
Subtract 9 kg from 17 kg to get 8 kg for 2 boxes. Divide by 2: 4 kg per box.
11. 2 identical boxes and a 1 kg weight balance 29 kg altogether. What is the mass of 1 box?
14 kg
Subtract 1 kg from 29 kg to get 28 kg for 2 boxes. Divide by 2: 14 kg per box.
12. 4 identical boxes and a 9 kg weight balance 45 kg altogether. What is the mass of 1 box?
9 kg
Subtract 9 kg from 45 kg to get 36 kg for 4 boxes. Divide by 4: 9 kg per box.

12 questions · Seed 46 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 7-9

Balance scale puzzles

Take your time. Show your thinking.

1. 6 identical boxes and a 12 kg weight balance 96 kg altogether. What is the mass of 1 box?
6 · 12 kg · 96 kg · 1 · Balance scale puzzles
2. 5 identical boxes and a 2 kg weight balance 67 kg altogether. What is the mass of 1 box?
5 · 2 kg · 67 kg · 1 · Balance scale puzzles
3. 6 identical boxes and a 5 kg weight balance 53 kg altogether. What is the mass of 1 box?
6 · 5 kg · 53 kg · 1 · Balance scale puzzles
4. 5 identical boxes and a 6 kg weight balance 46 kg altogether. What is the mass of 1 box?
5 · 6 kg · 46 kg · 1 · Balance scale puzzles
5. 3 identical boxes and a 4 kg weight balance 25 kg altogether. What is the mass of 1 box?
3 · 4 kg · 25 kg · 1 · Balance scale puzzles
6. 3 identical boxes and a 1 kg weight balance 10 kg altogether. What is the mass of 1 box?
3 · 1 kg · 10 kg · 1 · Balance scale puzzles
7. 2 identical boxes and a 5 kg weight balance 27 kg altogether. What is the mass of 1 box?
2 · 5 kg · 27 kg · 1 · Balance scale puzzles
8. 4 identical boxes and a 4 kg weight balance 12 kg altogether. What is the mass of 1 box?
4 · 4 kg · 12 kg · 1 · Balance scale puzzles
9. 5 identical boxes and a 8 kg weight balance 38 kg altogether. What is the mass of 1 box?
5 · 8 kg · 38 kg · 1 · Balance scale puzzles
10. 2 identical boxes and a 9 kg weight balance 17 kg altogether. What is the mass of 1 box?
2 · 9 kg · 17 kg · 1 · Balance scale puzzles
11. 2 identical boxes and a 1 kg weight balance 29 kg altogether. What is the mass of 1 box?
2 · 1 kg · 29 kg · 1 · Balance scale puzzles
12. 4 identical boxes and a 9 kg weight balance 45 kg altogether. What is the mass of 1 box?
4 · 9 kg · 45 kg · 1 · Balance scale puzzles

12 questions · Seed 46 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 7-9

Balance scale puzzles

Answers and reasoning. Review before teaching.

1. 6 identical boxes and a 12 kg weight balance 96 kg altogether. What is the mass of 1 box?
14 kg
Subtract 12 kg from 96 kg to get 84 kg for 6 boxes. Divide by 6: 14 kg per box.
2. 5 identical boxes and a 2 kg weight balance 67 kg altogether. What is the mass of 1 box?
13 kg
Subtract 2 kg from 67 kg to get 65 kg for 5 boxes. Divide by 5: 13 kg per box.
3. 6 identical boxes and a 5 kg weight balance 53 kg altogether. What is the mass of 1 box?
8 kg
Subtract 5 kg from 53 kg to get 48 kg for 6 boxes. Divide by 6: 8 kg per box.
4. 5 identical boxes and a 6 kg weight balance 46 kg altogether. What is the mass of 1 box?
8 kg
Subtract 6 kg from 46 kg to get 40 kg for 5 boxes. Divide by 5: 8 kg per box.
5. 3 identical boxes and a 4 kg weight balance 25 kg altogether. What is the mass of 1 box?
7 kg
Subtract 4 kg from 25 kg to get 21 kg for 3 boxes. Divide by 3: 7 kg per box.
6. 3 identical boxes and a 1 kg weight balance 10 kg altogether. What is the mass of 1 box?
3 kg
Subtract 1 kg from 10 kg to get 9 kg for 3 boxes. Divide by 3: 3 kg per box.
7. 2 identical boxes and a 5 kg weight balance 27 kg altogether. What is the mass of 1 box?
11 kg
Subtract 5 kg from 27 kg to get 22 kg for 2 boxes. Divide by 2: 11 kg per box.
8. 4 identical boxes and a 4 kg weight balance 12 kg altogether. What is the mass of 1 box?
2 kg
Subtract 4 kg from 12 kg to get 8 kg for 4 boxes. Divide by 4: 2 kg per box.
9. 5 identical boxes and a 8 kg weight balance 38 kg altogether. What is the mass of 1 box?
6 kg
Subtract 8 kg from 38 kg to get 30 kg for 5 boxes. Divide by 5: 6 kg per box.
10. 2 identical boxes and a 9 kg weight balance 17 kg altogether. What is the mass of 1 box?
4 kg
Subtract 9 kg from 17 kg to get 8 kg for 2 boxes. Divide by 2: 4 kg per box.
11. 2 identical boxes and a 1 kg weight balance 29 kg altogether. What is the mass of 1 box?
14 kg
Subtract 1 kg from 29 kg to get 28 kg for 2 boxes. Divide by 2: 14 kg per box.
12. 4 identical boxes and a 9 kg weight balance 45 kg altogether. What is the mass of 1 box?
9 kg
Subtract 9 kg from 45 kg to get 36 kg for 4 boxes. Divide by 4: 9 kg per box.

12 questions · Seed 46 · Age guidance, not curriculum certification