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. 3 identical boxes and a 1 kg weight balance 46 kg altogether. What is the mass of 1 box?
3 · 1 kg · 46 kg · 1 · Balance scale puzzles
2. 2 identical boxes and a 2 kg weight balance 28 kg altogether. What is the mass of 1 box?
2 · 2 kg · 28 kg · 1 · Balance scale puzzles
3. 3 identical boxes and a 9 kg weight balance 51 kg altogether. What is the mass of 1 box?
3 · 9 kg · 51 kg · 1 · Balance scale puzzles
4. 6 identical boxes and a 7 kg weight balance 97 kg altogether. What is the mass of 1 box?
6 · 7 kg · 97 kg · 1 · Balance scale puzzles
5. 6 identical boxes and a 6 kg weight balance 36 kg altogether. What is the mass of 1 box?
6 · 6 kg · 36 kg · 1 · Balance scale puzzles
6. 4 identical boxes and a 7 kg weight balance 43 kg altogether. What is the mass of 1 box?
4 · 7 kg · 43 kg · 1 · Balance scale puzzles
7. 3 identical boxes and a 5 kg weight balance 17 kg altogether. What is the mass of 1 box?
3 · 5 kg · 17 kg · 1 · Balance scale puzzles
8. 6 identical boxes and a 10 kg weight balance 70 kg altogether. What is the mass of 1 box?
6 · 10 kg · 70 kg · 1 · Balance scale puzzles
9. 5 identical boxes and a 10 kg weight balance 55 kg altogether. What is the mass of 1 box?
5 · 10 kg · 55 kg · 1 · Balance scale puzzles
10. 5 identical boxes and a 2 kg weight balance 77 kg altogether. What is the mass of 1 box?
5 · 2 kg · 77 kg · 1 · Balance scale puzzles
11. 2 identical boxes and a 11 kg weight balance 15 kg altogether. What is the mass of 1 box?
2 · 11 kg · 15 kg · 1 · Balance scale puzzles
12. 4 identical boxes and a 10 kg weight balance 70 kg altogether. What is the mass of 1 box?
4 · 10 kg · 70 kg · 1 · Balance scale puzzles

12 questions · Seed 48 · 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. 3 identical boxes and a 1 kg weight balance 46 kg altogether. What is the mass of 1 box?
15 kg
Subtract 1 kg from 46 kg to get 45 kg for 3 boxes. Divide by 3: 15 kg per box.
2. 2 identical boxes and a 2 kg weight balance 28 kg altogether. What is the mass of 1 box?
13 kg
Subtract 2 kg from 28 kg to get 26 kg for 2 boxes. Divide by 2: 13 kg per box.
3. 3 identical boxes and a 9 kg weight balance 51 kg altogether. What is the mass of 1 box?
14 kg
Subtract 9 kg from 51 kg to get 42 kg for 3 boxes. Divide by 3: 14 kg per box.
4. 6 identical boxes and a 7 kg weight balance 97 kg altogether. What is the mass of 1 box?
15 kg
Subtract 7 kg from 97 kg to get 90 kg for 6 boxes. Divide by 6: 15 kg per box.
5. 6 identical boxes and a 6 kg weight balance 36 kg altogether. What is the mass of 1 box?
5 kg
Subtract 6 kg from 36 kg to get 30 kg for 6 boxes. Divide by 6: 5 kg per box.
6. 4 identical boxes and a 7 kg weight balance 43 kg altogether. What is the mass of 1 box?
9 kg
Subtract 7 kg from 43 kg to get 36 kg for 4 boxes. Divide by 4: 9 kg per box.
7. 3 identical boxes and a 5 kg weight balance 17 kg altogether. What is the mass of 1 box?
4 kg
Subtract 5 kg from 17 kg to get 12 kg for 3 boxes. Divide by 3: 4 kg per box.
8. 6 identical boxes and a 10 kg weight balance 70 kg altogether. What is the mass of 1 box?
10 kg
Subtract 10 kg from 70 kg to get 60 kg for 6 boxes. Divide by 6: 10 kg per box.
9. 5 identical boxes and a 10 kg weight balance 55 kg altogether. What is the mass of 1 box?
9 kg
Subtract 10 kg from 55 kg to get 45 kg for 5 boxes. Divide by 5: 9 kg per box.
10. 5 identical boxes and a 2 kg weight balance 77 kg altogether. What is the mass of 1 box?
15 kg
Subtract 2 kg from 77 kg to get 75 kg for 5 boxes. Divide by 5: 15 kg per box.
11. 2 identical boxes and a 11 kg weight balance 15 kg altogether. What is the mass of 1 box?
2 kg
Subtract 11 kg from 15 kg to get 4 kg for 2 boxes. Divide by 2: 2 kg per box.
12. 4 identical boxes and a 10 kg weight balance 70 kg altogether. What is the mass of 1 box?
15 kg
Subtract 10 kg from 70 kg to get 60 kg for 4 boxes. Divide by 4: 15 kg per box.

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 7-9

Balance scale puzzles

Take your time. Show your thinking.

1. 3 identical boxes and a 1 kg weight balance 46 kg altogether. What is the mass of 1 box?
3 · 1 kg · 46 kg · 1 · Balance scale puzzles
2. 2 identical boxes and a 2 kg weight balance 28 kg altogether. What is the mass of 1 box?
2 · 2 kg · 28 kg · 1 · Balance scale puzzles
3. 3 identical boxes and a 9 kg weight balance 51 kg altogether. What is the mass of 1 box?
3 · 9 kg · 51 kg · 1 · Balance scale puzzles
4. 6 identical boxes and a 7 kg weight balance 97 kg altogether. What is the mass of 1 box?
6 · 7 kg · 97 kg · 1 · Balance scale puzzles
5. 6 identical boxes and a 6 kg weight balance 36 kg altogether. What is the mass of 1 box?
6 · 6 kg · 36 kg · 1 · Balance scale puzzles
6. 4 identical boxes and a 7 kg weight balance 43 kg altogether. What is the mass of 1 box?
4 · 7 kg · 43 kg · 1 · Balance scale puzzles
7. 3 identical boxes and a 5 kg weight balance 17 kg altogether. What is the mass of 1 box?
3 · 5 kg · 17 kg · 1 · Balance scale puzzles
8. 6 identical boxes and a 10 kg weight balance 70 kg altogether. What is the mass of 1 box?
6 · 10 kg · 70 kg · 1 · Balance scale puzzles
9. 5 identical boxes and a 10 kg weight balance 55 kg altogether. What is the mass of 1 box?
5 · 10 kg · 55 kg · 1 · Balance scale puzzles
10. 5 identical boxes and a 2 kg weight balance 77 kg altogether. What is the mass of 1 box?
5 · 2 kg · 77 kg · 1 · Balance scale puzzles
11. 2 identical boxes and a 11 kg weight balance 15 kg altogether. What is the mass of 1 box?
2 · 11 kg · 15 kg · 1 · Balance scale puzzles
12. 4 identical boxes and a 10 kg weight balance 70 kg altogether. What is the mass of 1 box?
4 · 10 kg · 70 kg · 1 · Balance scale puzzles

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 7-9

Balance scale puzzles

Answers and reasoning. Review before teaching.

1. 3 identical boxes and a 1 kg weight balance 46 kg altogether. What is the mass of 1 box?
15 kg
Subtract 1 kg from 46 kg to get 45 kg for 3 boxes. Divide by 3: 15 kg per box.
2. 2 identical boxes and a 2 kg weight balance 28 kg altogether. What is the mass of 1 box?
13 kg
Subtract 2 kg from 28 kg to get 26 kg for 2 boxes. Divide by 2: 13 kg per box.
3. 3 identical boxes and a 9 kg weight balance 51 kg altogether. What is the mass of 1 box?
14 kg
Subtract 9 kg from 51 kg to get 42 kg for 3 boxes. Divide by 3: 14 kg per box.
4. 6 identical boxes and a 7 kg weight balance 97 kg altogether. What is the mass of 1 box?
15 kg
Subtract 7 kg from 97 kg to get 90 kg for 6 boxes. Divide by 6: 15 kg per box.
5. 6 identical boxes and a 6 kg weight balance 36 kg altogether. What is the mass of 1 box?
5 kg
Subtract 6 kg from 36 kg to get 30 kg for 6 boxes. Divide by 6: 5 kg per box.
6. 4 identical boxes and a 7 kg weight balance 43 kg altogether. What is the mass of 1 box?
9 kg
Subtract 7 kg from 43 kg to get 36 kg for 4 boxes. Divide by 4: 9 kg per box.
7. 3 identical boxes and a 5 kg weight balance 17 kg altogether. What is the mass of 1 box?
4 kg
Subtract 5 kg from 17 kg to get 12 kg for 3 boxes. Divide by 3: 4 kg per box.
8. 6 identical boxes and a 10 kg weight balance 70 kg altogether. What is the mass of 1 box?
10 kg
Subtract 10 kg from 70 kg to get 60 kg for 6 boxes. Divide by 6: 10 kg per box.
9. 5 identical boxes and a 10 kg weight balance 55 kg altogether. What is the mass of 1 box?
9 kg
Subtract 10 kg from 55 kg to get 45 kg for 5 boxes. Divide by 5: 9 kg per box.
10. 5 identical boxes and a 2 kg weight balance 77 kg altogether. What is the mass of 1 box?
15 kg
Subtract 2 kg from 77 kg to get 75 kg for 5 boxes. Divide by 5: 15 kg per box.
11. 2 identical boxes and a 11 kg weight balance 15 kg altogether. What is the mass of 1 box?
2 kg
Subtract 11 kg from 15 kg to get 4 kg for 2 boxes. Divide by 2: 2 kg per box.
12. 4 identical boxes and a 10 kg weight balance 70 kg altogether. What is the mass of 1 box?
15 kg
Subtract 10 kg from 70 kg to get 60 kg for 4 boxes. Divide by 4: 15 kg per box.

12 questions · Seed 48 · Age guidance, not curriculum certification