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. 5 identical boxes and a 11 kg weight balance 26 kg altogether. What is the mass of 1 box?
5 · 11 kg · 26 kg · 1 · Balance scale puzzles
2. 2 identical boxes and a 5 kg weight balance 9 kg altogether. What is the mass of 1 box?
2 · 5 kg · 9 kg · 1 · Balance scale puzzles
3. 3 identical boxes and a 5 kg weight balance 47 kg altogether. What is the mass of 1 box?
3 · 5 kg · 47 kg · 1 · Balance scale puzzles
4. 3 identical boxes and a 7 kg weight balance 49 kg altogether. What is the mass of 1 box?
3 · 7 kg · 49 kg · 1 · Balance scale puzzles
5. 6 identical boxes and a 1 kg weight balance 85 kg altogether. What is the mass of 1 box?
6 · 1 kg · 85 kg · 1 · Balance scale puzzles
6. 2 identical boxes and a 2 kg weight balance 16 kg altogether. What is the mass of 1 box?
2 · 2 kg · 16 kg · 1 · Balance scale puzzles
7. 5 identical boxes and a 5 kg weight balance 45 kg altogether. What is the mass of 1 box?
5 · 5 kg · 45 kg · 1 · Balance scale puzzles
8. 6 identical boxes and a 3 kg weight balance 21 kg altogether. What is the mass of 1 box?
6 · 3 kg · 21 kg · 1 · Balance scale puzzles
9. 2 identical boxes and a 11 kg weight balance 31 kg altogether. What is the mass of 1 box?
2 · 11 kg · 31 kg · 1 · Balance scale puzzles
10. 2 identical boxes and a 4 kg weight balance 26 kg altogether. What is the mass of 1 box?
2 · 4 kg · 26 kg · 1 · Balance scale puzzles
11. 4 identical boxes and a 6 kg weight balance 58 kg altogether. What is the mass of 1 box?
4 · 6 kg · 58 kg · 1 · Balance scale puzzles
12. 5 identical boxes and a 2 kg weight balance 57 kg altogether. What is the mass of 1 box?
5 · 2 kg · 57 kg · 1 · Balance scale puzzles

12 questions · Seed 104729 · 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. 5 identical boxes and a 11 kg weight balance 26 kg altogether. What is the mass of 1 box?
3 kg
Subtract 11 kg from 26 kg to get 15 kg for 5 boxes. Divide by 5: 3 kg per box.
2. 2 identical boxes and a 5 kg weight balance 9 kg altogether. What is the mass of 1 box?
2 kg
Subtract 5 kg from 9 kg to get 4 kg for 2 boxes. Divide by 2: 2 kg per box.
3. 3 identical boxes and a 5 kg weight balance 47 kg altogether. What is the mass of 1 box?
14 kg
Subtract 5 kg from 47 kg to get 42 kg for 3 boxes. Divide by 3: 14 kg per box.
4. 3 identical boxes and a 7 kg weight balance 49 kg altogether. What is the mass of 1 box?
14 kg
Subtract 7 kg from 49 kg to get 42 kg for 3 boxes. Divide by 3: 14 kg per box.
5. 6 identical boxes and a 1 kg weight balance 85 kg altogether. What is the mass of 1 box?
14 kg
Subtract 1 kg from 85 kg to get 84 kg for 6 boxes. Divide by 6: 14 kg per box.
6. 2 identical boxes and a 2 kg weight balance 16 kg altogether. What is the mass of 1 box?
7 kg
Subtract 2 kg from 16 kg to get 14 kg for 2 boxes. Divide by 2: 7 kg per box.
7. 5 identical boxes and a 5 kg weight balance 45 kg altogether. What is the mass of 1 box?
8 kg
Subtract 5 kg from 45 kg to get 40 kg for 5 boxes. Divide by 5: 8 kg per box.
8. 6 identical boxes and a 3 kg weight balance 21 kg altogether. What is the mass of 1 box?
3 kg
Subtract 3 kg from 21 kg to get 18 kg for 6 boxes. Divide by 6: 3 kg per box.
9. 2 identical boxes and a 11 kg weight balance 31 kg altogether. What is the mass of 1 box?
10 kg
Subtract 11 kg from 31 kg to get 20 kg for 2 boxes. Divide by 2: 10 kg per box.
10. 2 identical boxes and a 4 kg weight balance 26 kg altogether. What is the mass of 1 box?
11 kg
Subtract 4 kg from 26 kg to get 22 kg for 2 boxes. Divide by 2: 11 kg per box.
11. 4 identical boxes and a 6 kg weight balance 58 kg altogether. What is the mass of 1 box?
13 kg
Subtract 6 kg from 58 kg to get 52 kg for 4 boxes. Divide by 4: 13 kg per box.
12. 5 identical boxes and a 2 kg weight balance 57 kg altogether. What is the mass of 1 box?
11 kg
Subtract 2 kg from 57 kg to get 55 kg for 5 boxes. Divide by 5: 11 kg per box.

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 7-9

Balance scale puzzles

Take your time. Show your thinking.

1. 5 identical boxes and a 11 kg weight balance 26 kg altogether. What is the mass of 1 box?
5 · 11 kg · 26 kg · 1 · Balance scale puzzles
2. 2 identical boxes and a 5 kg weight balance 9 kg altogether. What is the mass of 1 box?
2 · 5 kg · 9 kg · 1 · Balance scale puzzles
3. 3 identical boxes and a 5 kg weight balance 47 kg altogether. What is the mass of 1 box?
3 · 5 kg · 47 kg · 1 · Balance scale puzzles
4. 3 identical boxes and a 7 kg weight balance 49 kg altogether. What is the mass of 1 box?
3 · 7 kg · 49 kg · 1 · Balance scale puzzles
5. 6 identical boxes and a 1 kg weight balance 85 kg altogether. What is the mass of 1 box?
6 · 1 kg · 85 kg · 1 · Balance scale puzzles
6. 2 identical boxes and a 2 kg weight balance 16 kg altogether. What is the mass of 1 box?
2 · 2 kg · 16 kg · 1 · Balance scale puzzles
7. 5 identical boxes and a 5 kg weight balance 45 kg altogether. What is the mass of 1 box?
5 · 5 kg · 45 kg · 1 · Balance scale puzzles
8. 6 identical boxes and a 3 kg weight balance 21 kg altogether. What is the mass of 1 box?
6 · 3 kg · 21 kg · 1 · Balance scale puzzles
9. 2 identical boxes and a 11 kg weight balance 31 kg altogether. What is the mass of 1 box?
2 · 11 kg · 31 kg · 1 · Balance scale puzzles
10. 2 identical boxes and a 4 kg weight balance 26 kg altogether. What is the mass of 1 box?
2 · 4 kg · 26 kg · 1 · Balance scale puzzles
11. 4 identical boxes and a 6 kg weight balance 58 kg altogether. What is the mass of 1 box?
4 · 6 kg · 58 kg · 1 · Balance scale puzzles
12. 5 identical boxes and a 2 kg weight balance 57 kg altogether. What is the mass of 1 box?
5 · 2 kg · 57 kg · 1 · Balance scale puzzles

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 7-9

Balance scale puzzles

Answers and reasoning. Review before teaching.

1. 5 identical boxes and a 11 kg weight balance 26 kg altogether. What is the mass of 1 box?
3 kg
Subtract 11 kg from 26 kg to get 15 kg for 5 boxes. Divide by 5: 3 kg per box.
2. 2 identical boxes and a 5 kg weight balance 9 kg altogether. What is the mass of 1 box?
2 kg
Subtract 5 kg from 9 kg to get 4 kg for 2 boxes. Divide by 2: 2 kg per box.
3. 3 identical boxes and a 5 kg weight balance 47 kg altogether. What is the mass of 1 box?
14 kg
Subtract 5 kg from 47 kg to get 42 kg for 3 boxes. Divide by 3: 14 kg per box.
4. 3 identical boxes and a 7 kg weight balance 49 kg altogether. What is the mass of 1 box?
14 kg
Subtract 7 kg from 49 kg to get 42 kg for 3 boxes. Divide by 3: 14 kg per box.
5. 6 identical boxes and a 1 kg weight balance 85 kg altogether. What is the mass of 1 box?
14 kg
Subtract 1 kg from 85 kg to get 84 kg for 6 boxes. Divide by 6: 14 kg per box.
6. 2 identical boxes and a 2 kg weight balance 16 kg altogether. What is the mass of 1 box?
7 kg
Subtract 2 kg from 16 kg to get 14 kg for 2 boxes. Divide by 2: 7 kg per box.
7. 5 identical boxes and a 5 kg weight balance 45 kg altogether. What is the mass of 1 box?
8 kg
Subtract 5 kg from 45 kg to get 40 kg for 5 boxes. Divide by 5: 8 kg per box.
8. 6 identical boxes and a 3 kg weight balance 21 kg altogether. What is the mass of 1 box?
3 kg
Subtract 3 kg from 21 kg to get 18 kg for 6 boxes. Divide by 6: 3 kg per box.
9. 2 identical boxes and a 11 kg weight balance 31 kg altogether. What is the mass of 1 box?
10 kg
Subtract 11 kg from 31 kg to get 20 kg for 2 boxes. Divide by 2: 10 kg per box.
10. 2 identical boxes and a 4 kg weight balance 26 kg altogether. What is the mass of 1 box?
11 kg
Subtract 4 kg from 26 kg to get 22 kg for 2 boxes. Divide by 2: 11 kg per box.
11. 4 identical boxes and a 6 kg weight balance 58 kg altogether. What is the mass of 1 box?
13 kg
Subtract 6 kg from 58 kg to get 52 kg for 4 boxes. Divide by 4: 13 kg per box.
12. 5 identical boxes and a 2 kg weight balance 57 kg altogether. What is the mass of 1 box?
11 kg
Subtract 2 kg from 57 kg to get 55 kg for 5 boxes. Divide by 5: 11 kg per box.

12 questions · Seed 104729 · Age guidance, not curriculum certification