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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Worksheet StudioPractice pack · Ages 7-9

Balance scale puzzles

Take your time. Show your thinking.

1. 4 identical boxes and a 7 kg weight balance 55 kg altogether. What is the mass of 1 box?
4 · 7 kg · 55 kg · 1 · Balance scale puzzles
2. 2 identical boxes and a 9 kg weight balance 39 kg altogether. What is the mass of 1 box?
2 · 9 kg · 39 kg · 1 · Balance scale puzzles
3. 3 identical boxes and a 1 kg weight balance 40 kg altogether. What is the mass of 1 box?
3 · 1 kg · 40 kg · 1 · Balance scale puzzles
4. 6 identical boxes and a 10 kg weight balance 40 kg altogether. What is the mass of 1 box?
6 · 10 kg · 40 kg · 1 · Balance scale puzzles
5. 2 identical boxes and a 10 kg weight balance 24 kg altogether. What is the mass of 1 box?
2 · 10 kg · 24 kg · 1 · Balance scale puzzles
6. 3 identical boxes and a 6 kg weight balance 24 kg altogether. What is the mass of 1 box?
3 · 6 kg · 24 kg · 1 · Balance scale puzzles
7. 5 identical boxes and a 11 kg weight balance 56 kg altogether. What is the mass of 1 box?
5 · 11 kg · 56 kg · 1 · Balance scale puzzles
8. 5 identical boxes and a 10 kg weight balance 30 kg altogether. What is the mass of 1 box?
5 · 10 kg · 30 kg · 1 · Balance scale puzzles
9. 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
10. 6 identical boxes and a 2 kg weight balance 56 kg altogether. What is the mass of 1 box?
6 · 2 kg · 56 kg · 1 · Balance scale puzzles
11. 6 identical boxes and a 11 kg weight balance 89 kg altogether. What is the mass of 1 box?
6 · 11 kg · 89 kg · 1 · Balance scale puzzles
12. 3 identical boxes and a 9 kg weight balance 39 kg altogether. What is the mass of 1 box?
3 · 9 kg · 39 kg · 1 · Balance scale puzzles

12 questions · Seed 50 · 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. 4 identical boxes and a 7 kg weight balance 55 kg altogether. What is the mass of 1 box?
12 kg
Subtract 7 kg from 55 kg to get 48 kg for 4 boxes. Divide by 4: 12 kg per box.
2. 2 identical boxes and a 9 kg weight balance 39 kg altogether. What is the mass of 1 box?
15 kg
Subtract 9 kg from 39 kg to get 30 kg for 2 boxes. Divide by 2: 15 kg per box.
3. 3 identical boxes and a 1 kg weight balance 40 kg altogether. What is the mass of 1 box?
13 kg
Subtract 1 kg from 40 kg to get 39 kg for 3 boxes. Divide by 3: 13 kg per box.
4. 6 identical boxes and a 10 kg weight balance 40 kg altogether. What is the mass of 1 box?
5 kg
Subtract 10 kg from 40 kg to get 30 kg for 6 boxes. Divide by 6: 5 kg per box.
5. 2 identical boxes and a 10 kg weight balance 24 kg altogether. What is the mass of 1 box?
7 kg
Subtract 10 kg from 24 kg to get 14 kg for 2 boxes. Divide by 2: 7 kg per box.
6. 3 identical boxes and a 6 kg weight balance 24 kg altogether. What is the mass of 1 box?
6 kg
Subtract 6 kg from 24 kg to get 18 kg for 3 boxes. Divide by 3: 6 kg per box.
7. 5 identical boxes and a 11 kg weight balance 56 kg altogether. What is the mass of 1 box?
9 kg
Subtract 11 kg from 56 kg to get 45 kg for 5 boxes. Divide by 5: 9 kg per box.
8. 5 identical boxes and a 10 kg weight balance 30 kg altogether. What is the mass of 1 box?
4 kg
Subtract 10 kg from 30 kg to get 20 kg for 5 boxes. Divide by 5: 4 kg per box.
9. 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.
10. 6 identical boxes and a 2 kg weight balance 56 kg altogether. What is the mass of 1 box?
9 kg
Subtract 2 kg from 56 kg to get 54 kg for 6 boxes. Divide by 6: 9 kg per box.
11. 6 identical boxes and a 11 kg weight balance 89 kg altogether. What is the mass of 1 box?
13 kg
Subtract 11 kg from 89 kg to get 78 kg for 6 boxes. Divide by 6: 13 kg per box.
12. 3 identical boxes and a 9 kg weight balance 39 kg altogether. What is the mass of 1 box?
10 kg
Subtract 9 kg from 39 kg to get 30 kg for 3 boxes. Divide by 3: 10 kg per box.

12 questions · Seed 50 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 7-9

Balance scale puzzles

Take your time. Show your thinking.

1. 4 identical boxes and a 7 kg weight balance 55 kg altogether. What is the mass of 1 box?
4 · 7 kg · 55 kg · 1 · Balance scale puzzles
2. 2 identical boxes and a 9 kg weight balance 39 kg altogether. What is the mass of 1 box?
2 · 9 kg · 39 kg · 1 · Balance scale puzzles
3. 3 identical boxes and a 1 kg weight balance 40 kg altogether. What is the mass of 1 box?
3 · 1 kg · 40 kg · 1 · Balance scale puzzles
4. 6 identical boxes and a 10 kg weight balance 40 kg altogether. What is the mass of 1 box?
6 · 10 kg · 40 kg · 1 · Balance scale puzzles
5. 2 identical boxes and a 10 kg weight balance 24 kg altogether. What is the mass of 1 box?
2 · 10 kg · 24 kg · 1 · Balance scale puzzles
6. 3 identical boxes and a 6 kg weight balance 24 kg altogether. What is the mass of 1 box?
3 · 6 kg · 24 kg · 1 · Balance scale puzzles
7. 5 identical boxes and a 11 kg weight balance 56 kg altogether. What is the mass of 1 box?
5 · 11 kg · 56 kg · 1 · Balance scale puzzles
8. 5 identical boxes and a 10 kg weight balance 30 kg altogether. What is the mass of 1 box?
5 · 10 kg · 30 kg · 1 · Balance scale puzzles
9. 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
10. 6 identical boxes and a 2 kg weight balance 56 kg altogether. What is the mass of 1 box?
6 · 2 kg · 56 kg · 1 · Balance scale puzzles
11. 6 identical boxes and a 11 kg weight balance 89 kg altogether. What is the mass of 1 box?
6 · 11 kg · 89 kg · 1 · Balance scale puzzles
12. 3 identical boxes and a 9 kg weight balance 39 kg altogether. What is the mass of 1 box?
3 · 9 kg · 39 kg · 1 · Balance scale puzzles

12 questions · Seed 50 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 7-9

Balance scale puzzles

Answers and reasoning. Review before teaching.

1. 4 identical boxes and a 7 kg weight balance 55 kg altogether. What is the mass of 1 box?
12 kg
Subtract 7 kg from 55 kg to get 48 kg for 4 boxes. Divide by 4: 12 kg per box.
2. 2 identical boxes and a 9 kg weight balance 39 kg altogether. What is the mass of 1 box?
15 kg
Subtract 9 kg from 39 kg to get 30 kg for 2 boxes. Divide by 2: 15 kg per box.
3. 3 identical boxes and a 1 kg weight balance 40 kg altogether. What is the mass of 1 box?
13 kg
Subtract 1 kg from 40 kg to get 39 kg for 3 boxes. Divide by 3: 13 kg per box.
4. 6 identical boxes and a 10 kg weight balance 40 kg altogether. What is the mass of 1 box?
5 kg
Subtract 10 kg from 40 kg to get 30 kg for 6 boxes. Divide by 6: 5 kg per box.
5. 2 identical boxes and a 10 kg weight balance 24 kg altogether. What is the mass of 1 box?
7 kg
Subtract 10 kg from 24 kg to get 14 kg for 2 boxes. Divide by 2: 7 kg per box.
6. 3 identical boxes and a 6 kg weight balance 24 kg altogether. What is the mass of 1 box?
6 kg
Subtract 6 kg from 24 kg to get 18 kg for 3 boxes. Divide by 3: 6 kg per box.
7. 5 identical boxes and a 11 kg weight balance 56 kg altogether. What is the mass of 1 box?
9 kg
Subtract 11 kg from 56 kg to get 45 kg for 5 boxes. Divide by 5: 9 kg per box.
8. 5 identical boxes and a 10 kg weight balance 30 kg altogether. What is the mass of 1 box?
4 kg
Subtract 10 kg from 30 kg to get 20 kg for 5 boxes. Divide by 5: 4 kg per box.
9. 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.
10. 6 identical boxes and a 2 kg weight balance 56 kg altogether. What is the mass of 1 box?
9 kg
Subtract 2 kg from 56 kg to get 54 kg for 6 boxes. Divide by 6: 9 kg per box.
11. 6 identical boxes and a 11 kg weight balance 89 kg altogether. What is the mass of 1 box?
13 kg
Subtract 11 kg from 89 kg to get 78 kg for 6 boxes. Divide by 6: 13 kg per box.
12. 3 identical boxes and a 9 kg weight balance 39 kg altogether. What is the mass of 1 box?
10 kg
Subtract 9 kg from 39 kg to get 30 kg for 3 boxes. Divide by 3: 10 kg per box.

12 questions · Seed 50 · Age guidance, not curriculum certification