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. 6 identical boxes and a 4 kg weight balance 40 kg altogether. What is the mass of 1 box?
6 · 4 kg · 40 kg · 1 · Balance scale puzzles
2. 5 identical boxes and a 8 kg weight balance 33 kg altogether. What is the mass of 1 box?
5 · 8 kg · 33 kg · 1 · Balance scale puzzles
3. 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
4. 6 identical boxes and a 1 kg weight balance 73 kg altogether. What is the mass of 1 box?
6 · 1 kg · 73 kg · 1 · Balance scale puzzles
5. 3 identical boxes and a 6 kg weight balance 15 kg altogether. What is the mass of 1 box?
3 · 6 kg · 15 kg · 1 · Balance scale puzzles
6. 5 identical boxes and a 11 kg weight balance 76 kg altogether. What is the mass of 1 box?
5 · 11 kg · 76 kg · 1 · Balance scale puzzles
7. 3 identical boxes and a 3 kg weight balance 30 kg altogether. What is the mass of 1 box?
3 · 3 kg · 30 kg · 1 · Balance scale puzzles
8. 5 identical boxes and a 10 kg weight balance 85 kg altogether. What is the mass of 1 box?
5 · 10 kg · 85 kg · 1 · Balance scale puzzles
9. 4 identical boxes and a 3 kg weight balance 43 kg altogether. What is the mass of 1 box?
4 · 3 kg · 43 kg · 1 · Balance scale puzzles
10. 3 identical boxes and a 3 kg weight balance 9 kg altogether. What is the mass of 1 box?
3 · 3 kg · 9 kg · 1 · Balance scale puzzles
11. 5 identical boxes and a 8 kg weight balance 53 kg altogether. What is the mass of 1 box?
5 · 8 kg · 53 kg · 1 · Balance scale puzzles
12. 3 identical boxes and a 1 kg weight balance 43 kg altogether. What is the mass of 1 box?
3 · 1 kg · 43 kg · 1 · Balance scale puzzles

12 questions · Seed 45 · 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 4 kg weight balance 40 kg altogether. What is the mass of 1 box?
6 kg
Subtract 4 kg from 40 kg to get 36 kg for 6 boxes. Divide by 6: 6 kg per box.
2. 5 identical boxes and a 8 kg weight balance 33 kg altogether. What is the mass of 1 box?
5 kg
Subtract 8 kg from 33 kg to get 25 kg for 5 boxes. Divide by 5: 5 kg per box.
3. 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.
4. 6 identical boxes and a 1 kg weight balance 73 kg altogether. What is the mass of 1 box?
12 kg
Subtract 1 kg from 73 kg to get 72 kg for 6 boxes. Divide by 6: 12 kg per box.
5. 3 identical boxes and a 6 kg weight balance 15 kg altogether. What is the mass of 1 box?
3 kg
Subtract 6 kg from 15 kg to get 9 kg for 3 boxes. Divide by 3: 3 kg per box.
6. 5 identical boxes and a 11 kg weight balance 76 kg altogether. What is the mass of 1 box?
13 kg
Subtract 11 kg from 76 kg to get 65 kg for 5 boxes. Divide by 5: 13 kg per box.
7. 3 identical boxes and a 3 kg weight balance 30 kg altogether. What is the mass of 1 box?
9 kg
Subtract 3 kg from 30 kg to get 27 kg for 3 boxes. Divide by 3: 9 kg per box.
8. 5 identical boxes and a 10 kg weight balance 85 kg altogether. What is the mass of 1 box?
15 kg
Subtract 10 kg from 85 kg to get 75 kg for 5 boxes. Divide by 5: 15 kg per box.
9. 4 identical boxes and a 3 kg weight balance 43 kg altogether. What is the mass of 1 box?
10 kg
Subtract 3 kg from 43 kg to get 40 kg for 4 boxes. Divide by 4: 10 kg per box.
10. 3 identical boxes and a 3 kg weight balance 9 kg altogether. What is the mass of 1 box?
2 kg
Subtract 3 kg from 9 kg to get 6 kg for 3 boxes. Divide by 3: 2 kg per box.
11. 5 identical boxes and a 8 kg weight balance 53 kg altogether. What is the mass of 1 box?
9 kg
Subtract 8 kg from 53 kg to get 45 kg for 5 boxes. Divide by 5: 9 kg per box.
12. 3 identical boxes and a 1 kg weight balance 43 kg altogether. What is the mass of 1 box?
14 kg
Subtract 1 kg from 43 kg to get 42 kg for 3 boxes. Divide by 3: 14 kg per box.

12 questions · Seed 45 · 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 4 kg weight balance 40 kg altogether. What is the mass of 1 box?
6 · 4 kg · 40 kg · 1 · Balance scale puzzles
2. 5 identical boxes and a 8 kg weight balance 33 kg altogether. What is the mass of 1 box?
5 · 8 kg · 33 kg · 1 · Balance scale puzzles
3. 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
4. 6 identical boxes and a 1 kg weight balance 73 kg altogether. What is the mass of 1 box?
6 · 1 kg · 73 kg · 1 · Balance scale puzzles
5. 3 identical boxes and a 6 kg weight balance 15 kg altogether. What is the mass of 1 box?
3 · 6 kg · 15 kg · 1 · Balance scale puzzles
6. 5 identical boxes and a 11 kg weight balance 76 kg altogether. What is the mass of 1 box?
5 · 11 kg · 76 kg · 1 · Balance scale puzzles
7. 3 identical boxes and a 3 kg weight balance 30 kg altogether. What is the mass of 1 box?
3 · 3 kg · 30 kg · 1 · Balance scale puzzles
8. 5 identical boxes and a 10 kg weight balance 85 kg altogether. What is the mass of 1 box?
5 · 10 kg · 85 kg · 1 · Balance scale puzzles
9. 4 identical boxes and a 3 kg weight balance 43 kg altogether. What is the mass of 1 box?
4 · 3 kg · 43 kg · 1 · Balance scale puzzles
10. 3 identical boxes and a 3 kg weight balance 9 kg altogether. What is the mass of 1 box?
3 · 3 kg · 9 kg · 1 · Balance scale puzzles
11. 5 identical boxes and a 8 kg weight balance 53 kg altogether. What is the mass of 1 box?
5 · 8 kg · 53 kg · 1 · Balance scale puzzles
12. 3 identical boxes and a 1 kg weight balance 43 kg altogether. What is the mass of 1 box?
3 · 1 kg · 43 kg · 1 · Balance scale puzzles

12 questions · Seed 45 · 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 4 kg weight balance 40 kg altogether. What is the mass of 1 box?
6 kg
Subtract 4 kg from 40 kg to get 36 kg for 6 boxes. Divide by 6: 6 kg per box.
2. 5 identical boxes and a 8 kg weight balance 33 kg altogether. What is the mass of 1 box?
5 kg
Subtract 8 kg from 33 kg to get 25 kg for 5 boxes. Divide by 5: 5 kg per box.
3. 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.
4. 6 identical boxes and a 1 kg weight balance 73 kg altogether. What is the mass of 1 box?
12 kg
Subtract 1 kg from 73 kg to get 72 kg for 6 boxes. Divide by 6: 12 kg per box.
5. 3 identical boxes and a 6 kg weight balance 15 kg altogether. What is the mass of 1 box?
3 kg
Subtract 6 kg from 15 kg to get 9 kg for 3 boxes. Divide by 3: 3 kg per box.
6. 5 identical boxes and a 11 kg weight balance 76 kg altogether. What is the mass of 1 box?
13 kg
Subtract 11 kg from 76 kg to get 65 kg for 5 boxes. Divide by 5: 13 kg per box.
7. 3 identical boxes and a 3 kg weight balance 30 kg altogether. What is the mass of 1 box?
9 kg
Subtract 3 kg from 30 kg to get 27 kg for 3 boxes. Divide by 3: 9 kg per box.
8. 5 identical boxes and a 10 kg weight balance 85 kg altogether. What is the mass of 1 box?
15 kg
Subtract 10 kg from 85 kg to get 75 kg for 5 boxes. Divide by 5: 15 kg per box.
9. 4 identical boxes and a 3 kg weight balance 43 kg altogether. What is the mass of 1 box?
10 kg
Subtract 3 kg from 43 kg to get 40 kg for 4 boxes. Divide by 4: 10 kg per box.
10. 3 identical boxes and a 3 kg weight balance 9 kg altogether. What is the mass of 1 box?
2 kg
Subtract 3 kg from 9 kg to get 6 kg for 3 boxes. Divide by 3: 2 kg per box.
11. 5 identical boxes and a 8 kg weight balance 53 kg altogether. What is the mass of 1 box?
9 kg
Subtract 8 kg from 53 kg to get 45 kg for 5 boxes. Divide by 5: 9 kg per box.
12. 3 identical boxes and a 1 kg weight balance 43 kg altogether. What is the mass of 1 box?
14 kg
Subtract 1 kg from 43 kg to get 42 kg for 3 boxes. Divide by 3: 14 kg per box.

12 questions · Seed 45 · Age guidance, not curriculum certification