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. 6 identical boxes and a 9 kg weight balance 39 kg altogether. What is the mass of 1 box?
6 · 9 kg · 39 kg · 1 · Balance scale puzzles
2. 4 identical boxes and a 10 kg weight balance 42 kg altogether. What is the mass of 1 box?
4 · 10 kg · 42 kg · 1 · Balance scale puzzles
3. 6 identical boxes and a 12 kg weight balance 84 kg altogether. What is the mass of 1 box?
6 · 12 kg · 84 kg · 1 · Balance scale puzzles
4. 6 identical boxes and a 2 kg weight balance 74 kg altogether. What is the mass of 1 box?
6 · 2 kg · 74 kg · 1 · Balance scale puzzles
5. 3 identical boxes and a 8 kg weight balance 38 kg altogether. What is the mass of 1 box?
3 · 8 kg · 38 kg · 1 · Balance scale puzzles
6. 2 identical boxes and a 2 kg weight balance 18 kg altogether. What is the mass of 1 box?
2 · 2 kg · 18 kg · 1 · Balance scale puzzles
7. 4 identical boxes and a 10 kg weight balance 46 kg altogether. What is the mass of 1 box?
4 · 10 kg · 46 kg · 1 · Balance scale puzzles
8. 6 identical boxes and a 8 kg weight balance 86 kg altogether. What is the mass of 1 box?
6 · 8 kg · 86 kg · 1 · Balance scale puzzles
9. 4 identical boxes and a 11 kg weight balance 59 kg altogether. What is the mass of 1 box?
4 · 11 kg · 59 kg · 1 · Balance scale puzzles
10. 6 identical boxes and a 10 kg weight balance 76 kg altogether. What is the mass of 1 box?
6 · 10 kg · 76 kg · 1 · Balance scale puzzles
11. 4 identical boxes and a 7 kg weight balance 47 kg altogether. What is the mass of 1 box?
4 · 7 kg · 47 kg · 1 · Balance scale puzzles
12. 4 identical boxes and a 7 kg weight balance 59 kg altogether. What is the mass of 1 box?
4 · 7 kg · 59 kg · 1 · Balance scale puzzles

12 questions · Seed 49 · 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 9 kg weight balance 39 kg altogether. What is the mass of 1 box?
5 kg
Subtract 9 kg from 39 kg to get 30 kg for 6 boxes. Divide by 6: 5 kg per box.
2. 4 identical boxes and a 10 kg weight balance 42 kg altogether. What is the mass of 1 box?
8 kg
Subtract 10 kg from 42 kg to get 32 kg for 4 boxes. Divide by 4: 8 kg per box.
3. 6 identical boxes and a 12 kg weight balance 84 kg altogether. What is the mass of 1 box?
12 kg
Subtract 12 kg from 84 kg to get 72 kg for 6 boxes. Divide by 6: 12 kg per box.
4. 6 identical boxes and a 2 kg weight balance 74 kg altogether. What is the mass of 1 box?
12 kg
Subtract 2 kg from 74 kg to get 72 kg for 6 boxes. Divide by 6: 12 kg per box.
5. 3 identical boxes and a 8 kg weight balance 38 kg altogether. What is the mass of 1 box?
10 kg
Subtract 8 kg from 38 kg to get 30 kg for 3 boxes. Divide by 3: 10 kg per box.
6. 2 identical boxes and a 2 kg weight balance 18 kg altogether. What is the mass of 1 box?
8 kg
Subtract 2 kg from 18 kg to get 16 kg for 2 boxes. Divide by 2: 8 kg per box.
7. 4 identical boxes and a 10 kg weight balance 46 kg altogether. What is the mass of 1 box?
9 kg
Subtract 10 kg from 46 kg to get 36 kg for 4 boxes. Divide by 4: 9 kg per box.
8. 6 identical boxes and a 8 kg weight balance 86 kg altogether. What is the mass of 1 box?
13 kg
Subtract 8 kg from 86 kg to get 78 kg for 6 boxes. Divide by 6: 13 kg per box.
9. 4 identical boxes and a 11 kg weight balance 59 kg altogether. What is the mass of 1 box?
12 kg
Subtract 11 kg from 59 kg to get 48 kg for 4 boxes. Divide by 4: 12 kg per box.
10. 6 identical boxes and a 10 kg weight balance 76 kg altogether. What is the mass of 1 box?
11 kg
Subtract 10 kg from 76 kg to get 66 kg for 6 boxes. Divide by 6: 11 kg per box.
11. 4 identical boxes and a 7 kg weight balance 47 kg altogether. What is the mass of 1 box?
10 kg
Subtract 7 kg from 47 kg to get 40 kg for 4 boxes. Divide by 4: 10 kg per box.
12. 4 identical boxes and a 7 kg weight balance 59 kg altogether. What is the mass of 1 box?
13 kg
Subtract 7 kg from 59 kg to get 52 kg for 4 boxes. Divide by 4: 13 kg per box.

12 questions · Seed 49 · 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 9 kg weight balance 39 kg altogether. What is the mass of 1 box?
6 · 9 kg · 39 kg · 1 · Balance scale puzzles
2. 4 identical boxes and a 10 kg weight balance 42 kg altogether. What is the mass of 1 box?
4 · 10 kg · 42 kg · 1 · Balance scale puzzles
3. 6 identical boxes and a 12 kg weight balance 84 kg altogether. What is the mass of 1 box?
6 · 12 kg · 84 kg · 1 · Balance scale puzzles
4. 6 identical boxes and a 2 kg weight balance 74 kg altogether. What is the mass of 1 box?
6 · 2 kg · 74 kg · 1 · Balance scale puzzles
5. 3 identical boxes and a 8 kg weight balance 38 kg altogether. What is the mass of 1 box?
3 · 8 kg · 38 kg · 1 · Balance scale puzzles
6. 2 identical boxes and a 2 kg weight balance 18 kg altogether. What is the mass of 1 box?
2 · 2 kg · 18 kg · 1 · Balance scale puzzles
7. 4 identical boxes and a 10 kg weight balance 46 kg altogether. What is the mass of 1 box?
4 · 10 kg · 46 kg · 1 · Balance scale puzzles
8. 6 identical boxes and a 8 kg weight balance 86 kg altogether. What is the mass of 1 box?
6 · 8 kg · 86 kg · 1 · Balance scale puzzles
9. 4 identical boxes and a 11 kg weight balance 59 kg altogether. What is the mass of 1 box?
4 · 11 kg · 59 kg · 1 · Balance scale puzzles
10. 6 identical boxes and a 10 kg weight balance 76 kg altogether. What is the mass of 1 box?
6 · 10 kg · 76 kg · 1 · Balance scale puzzles
11. 4 identical boxes and a 7 kg weight balance 47 kg altogether. What is the mass of 1 box?
4 · 7 kg · 47 kg · 1 · Balance scale puzzles
12. 4 identical boxes and a 7 kg weight balance 59 kg altogether. What is the mass of 1 box?
4 · 7 kg · 59 kg · 1 · Balance scale puzzles

12 questions · Seed 49 · 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 9 kg weight balance 39 kg altogether. What is the mass of 1 box?
5 kg
Subtract 9 kg from 39 kg to get 30 kg for 6 boxes. Divide by 6: 5 kg per box.
2. 4 identical boxes and a 10 kg weight balance 42 kg altogether. What is the mass of 1 box?
8 kg
Subtract 10 kg from 42 kg to get 32 kg for 4 boxes. Divide by 4: 8 kg per box.
3. 6 identical boxes and a 12 kg weight balance 84 kg altogether. What is the mass of 1 box?
12 kg
Subtract 12 kg from 84 kg to get 72 kg for 6 boxes. Divide by 6: 12 kg per box.
4. 6 identical boxes and a 2 kg weight balance 74 kg altogether. What is the mass of 1 box?
12 kg
Subtract 2 kg from 74 kg to get 72 kg for 6 boxes. Divide by 6: 12 kg per box.
5. 3 identical boxes and a 8 kg weight balance 38 kg altogether. What is the mass of 1 box?
10 kg
Subtract 8 kg from 38 kg to get 30 kg for 3 boxes. Divide by 3: 10 kg per box.
6. 2 identical boxes and a 2 kg weight balance 18 kg altogether. What is the mass of 1 box?
8 kg
Subtract 2 kg from 18 kg to get 16 kg for 2 boxes. Divide by 2: 8 kg per box.
7. 4 identical boxes and a 10 kg weight balance 46 kg altogether. What is the mass of 1 box?
9 kg
Subtract 10 kg from 46 kg to get 36 kg for 4 boxes. Divide by 4: 9 kg per box.
8. 6 identical boxes and a 8 kg weight balance 86 kg altogether. What is the mass of 1 box?
13 kg
Subtract 8 kg from 86 kg to get 78 kg for 6 boxes. Divide by 6: 13 kg per box.
9. 4 identical boxes and a 11 kg weight balance 59 kg altogether. What is the mass of 1 box?
12 kg
Subtract 11 kg from 59 kg to get 48 kg for 4 boxes. Divide by 4: 12 kg per box.
10. 6 identical boxes and a 10 kg weight balance 76 kg altogether. What is the mass of 1 box?
11 kg
Subtract 10 kg from 76 kg to get 66 kg for 6 boxes. Divide by 6: 11 kg per box.
11. 4 identical boxes and a 7 kg weight balance 47 kg altogether. What is the mass of 1 box?
10 kg
Subtract 7 kg from 47 kg to get 40 kg for 4 boxes. Divide by 4: 10 kg per box.
12. 4 identical boxes and a 7 kg weight balance 59 kg altogether. What is the mass of 1 box?
13 kg
Subtract 7 kg from 59 kg to get 52 kg for 4 boxes. Divide by 4: 13 kg per box.

12 questions · Seed 49 · Age guidance, not curriculum certification