ReasoningAges 10-12

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 10-12

Balance scale puzzles

Take your time. Show your thinking.

1. 5 identical boxes and a 9 kg weight balance 54 kg altogether. What is the mass of 1 box?
5 · 9 kg · 54 kg · 1 · Balance scale puzzles
2. 5 identical boxes and a 1 kg weight balance 21 kg altogether. What is the mass of 1 box?
5 · 1 kg · 21 kg · 1 · Balance scale puzzles
3. 5 identical boxes and a 11 kg weight balance 86 kg altogether. What is the mass of 1 box?
5 · 11 kg · 86 kg · 1 · Balance scale puzzles
4. 2 identical boxes and a 10 kg weight balance 26 kg altogether. What is the mass of 1 box?
2 · 10 kg · 26 kg · 1 · Balance scale puzzles
5. 6 identical boxes and a 1 kg weight balance 13 kg altogether. What is the mass of 1 box?
6 · 1 kg · 13 kg · 1 · Balance scale puzzles
6. 5 identical boxes and a 12 kg weight balance 87 kg altogether. What is the mass of 1 box?
5 · 12 kg · 87 kg · 1 · Balance scale puzzles
7. 6 identical boxes and a 9 kg weight balance 33 kg altogether. What is the mass of 1 box?
6 · 9 kg · 33 kg · 1 · Balance scale puzzles
8. 6 identical boxes and a 10 kg weight balance 52 kg altogether. What is the mass of 1 box?
6 · 10 kg · 52 kg · 1 · Balance scale puzzles
9. 5 identical boxes and a 11 kg weight balance 36 kg altogether. What is the mass of 1 box?
5 · 11 kg · 36 kg · 1 · Balance scale puzzles
10. 2 identical boxes and a 3 kg weight balance 19 kg altogether. What is the mass of 1 box?
2 · 3 kg · 19 kg · 1 · Balance scale puzzles
11. 5 identical boxes and a 8 kg weight balance 68 kg altogether. What is the mass of 1 box?
5 · 8 kg · 68 kg · 1 · Balance scale puzzles
12. 3 identical boxes and a 2 kg weight balance 17 kg altogether. What is the mass of 1 box?
3 · 2 kg · 17 kg · 1 · Balance scale puzzles

12 questions · Seed 43 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Balance scale puzzles

Answers and reasoning. Review before teaching.

1. 5 identical boxes and a 9 kg weight balance 54 kg altogether. What is the mass of 1 box?
9 kg
Subtract 9 kg from 54 kg to get 45 kg for 5 boxes. Divide by 5: 9 kg per box.
2. 5 identical boxes and a 1 kg weight balance 21 kg altogether. What is the mass of 1 box?
4 kg
Subtract 1 kg from 21 kg to get 20 kg for 5 boxes. Divide by 5: 4 kg per box.
3. 5 identical boxes and a 11 kg weight balance 86 kg altogether. What is the mass of 1 box?
15 kg
Subtract 11 kg from 86 kg to get 75 kg for 5 boxes. Divide by 5: 15 kg per box.
4. 2 identical boxes and a 10 kg weight balance 26 kg altogether. What is the mass of 1 box?
8 kg
Subtract 10 kg from 26 kg to get 16 kg for 2 boxes. Divide by 2: 8 kg per box.
5. 6 identical boxes and a 1 kg weight balance 13 kg altogether. What is the mass of 1 box?
2 kg
Subtract 1 kg from 13 kg to get 12 kg for 6 boxes. Divide by 6: 2 kg per box.
6. 5 identical boxes and a 12 kg weight balance 87 kg altogether. What is the mass of 1 box?
15 kg
Subtract 12 kg from 87 kg to get 75 kg for 5 boxes. Divide by 5: 15 kg per box.
7. 6 identical boxes and a 9 kg weight balance 33 kg altogether. What is the mass of 1 box?
4 kg
Subtract 9 kg from 33 kg to get 24 kg for 6 boxes. Divide by 6: 4 kg per box.
8. 6 identical boxes and a 10 kg weight balance 52 kg altogether. What is the mass of 1 box?
7 kg
Subtract 10 kg from 52 kg to get 42 kg for 6 boxes. Divide by 6: 7 kg per box.
9. 5 identical boxes and a 11 kg weight balance 36 kg altogether. What is the mass of 1 box?
5 kg
Subtract 11 kg from 36 kg to get 25 kg for 5 boxes. Divide by 5: 5 kg per box.
10. 2 identical boxes and a 3 kg weight balance 19 kg altogether. What is the mass of 1 box?
8 kg
Subtract 3 kg from 19 kg to get 16 kg for 2 boxes. Divide by 2: 8 kg per box.
11. 5 identical boxes and a 8 kg weight balance 68 kg altogether. What is the mass of 1 box?
12 kg
Subtract 8 kg from 68 kg to get 60 kg for 5 boxes. Divide by 5: 12 kg per box.
12. 3 identical boxes and a 2 kg weight balance 17 kg altogether. What is the mass of 1 box?
5 kg
Subtract 2 kg from 17 kg to get 15 kg for 3 boxes. Divide by 3: 5 kg per box.

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Balance scale puzzles

Take your time. Show your thinking.

1. 5 identical boxes and a 9 kg weight balance 54 kg altogether. What is the mass of 1 box?
5 · 9 kg · 54 kg · 1 · Balance scale puzzles
2. 5 identical boxes and a 1 kg weight balance 21 kg altogether. What is the mass of 1 box?
5 · 1 kg · 21 kg · 1 · Balance scale puzzles
3. 5 identical boxes and a 11 kg weight balance 86 kg altogether. What is the mass of 1 box?
5 · 11 kg · 86 kg · 1 · Balance scale puzzles
4. 2 identical boxes and a 10 kg weight balance 26 kg altogether. What is the mass of 1 box?
2 · 10 kg · 26 kg · 1 · Balance scale puzzles
5. 6 identical boxes and a 1 kg weight balance 13 kg altogether. What is the mass of 1 box?
6 · 1 kg · 13 kg · 1 · Balance scale puzzles
6. 5 identical boxes and a 12 kg weight balance 87 kg altogether. What is the mass of 1 box?
5 · 12 kg · 87 kg · 1 · Balance scale puzzles
7. 6 identical boxes and a 9 kg weight balance 33 kg altogether. What is the mass of 1 box?
6 · 9 kg · 33 kg · 1 · Balance scale puzzles
8. 6 identical boxes and a 10 kg weight balance 52 kg altogether. What is the mass of 1 box?
6 · 10 kg · 52 kg · 1 · Balance scale puzzles
9. 5 identical boxes and a 11 kg weight balance 36 kg altogether. What is the mass of 1 box?
5 · 11 kg · 36 kg · 1 · Balance scale puzzles
10. 2 identical boxes and a 3 kg weight balance 19 kg altogether. What is the mass of 1 box?
2 · 3 kg · 19 kg · 1 · Balance scale puzzles
11. 5 identical boxes and a 8 kg weight balance 68 kg altogether. What is the mass of 1 box?
5 · 8 kg · 68 kg · 1 · Balance scale puzzles
12. 3 identical boxes and a 2 kg weight balance 17 kg altogether. What is the mass of 1 box?
3 · 2 kg · 17 kg · 1 · Balance scale puzzles

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Balance scale puzzles

Answers and reasoning. Review before teaching.

1. 5 identical boxes and a 9 kg weight balance 54 kg altogether. What is the mass of 1 box?
9 kg
Subtract 9 kg from 54 kg to get 45 kg for 5 boxes. Divide by 5: 9 kg per box.
2. 5 identical boxes and a 1 kg weight balance 21 kg altogether. What is the mass of 1 box?
4 kg
Subtract 1 kg from 21 kg to get 20 kg for 5 boxes. Divide by 5: 4 kg per box.
3. 5 identical boxes and a 11 kg weight balance 86 kg altogether. What is the mass of 1 box?
15 kg
Subtract 11 kg from 86 kg to get 75 kg for 5 boxes. Divide by 5: 15 kg per box.
4. 2 identical boxes and a 10 kg weight balance 26 kg altogether. What is the mass of 1 box?
8 kg
Subtract 10 kg from 26 kg to get 16 kg for 2 boxes. Divide by 2: 8 kg per box.
5. 6 identical boxes and a 1 kg weight balance 13 kg altogether. What is the mass of 1 box?
2 kg
Subtract 1 kg from 13 kg to get 12 kg for 6 boxes. Divide by 6: 2 kg per box.
6. 5 identical boxes and a 12 kg weight balance 87 kg altogether. What is the mass of 1 box?
15 kg
Subtract 12 kg from 87 kg to get 75 kg for 5 boxes. Divide by 5: 15 kg per box.
7. 6 identical boxes and a 9 kg weight balance 33 kg altogether. What is the mass of 1 box?
4 kg
Subtract 9 kg from 33 kg to get 24 kg for 6 boxes. Divide by 6: 4 kg per box.
8. 6 identical boxes and a 10 kg weight balance 52 kg altogether. What is the mass of 1 box?
7 kg
Subtract 10 kg from 52 kg to get 42 kg for 6 boxes. Divide by 6: 7 kg per box.
9. 5 identical boxes and a 11 kg weight balance 36 kg altogether. What is the mass of 1 box?
5 kg
Subtract 11 kg from 36 kg to get 25 kg for 5 boxes. Divide by 5: 5 kg per box.
10. 2 identical boxes and a 3 kg weight balance 19 kg altogether. What is the mass of 1 box?
8 kg
Subtract 3 kg from 19 kg to get 16 kg for 2 boxes. Divide by 2: 8 kg per box.
11. 5 identical boxes and a 8 kg weight balance 68 kg altogether. What is the mass of 1 box?
12 kg
Subtract 8 kg from 68 kg to get 60 kg for 5 boxes. Divide by 5: 12 kg per box.
12. 3 identical boxes and a 2 kg weight balance 17 kg altogether. What is the mass of 1 box?
5 kg
Subtract 2 kg from 17 kg to get 15 kg for 3 boxes. Divide by 3: 5 kg per box.

12 questions · Seed 43 · Age guidance, not curriculum certification