ReasoningAges 10-12

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.

New variation Try interactive challenge Browse templates

Age band:Ages 7-9 Ages 10-12

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 10-12

Balance scale puzzles

Take your time. Show your thinking.

1. 4 identical boxes and a 7 kg weight balance 23 kg altogether. What is the mass of 1 box?
4 · 7 kg · 23 kg · 1 · Balance scale puzzles
2. 3 identical boxes and a 3 kg weight balance 18 kg altogether. What is the mass of 1 box?
3 · 3 kg · 18 kg · 1 · Balance scale puzzles
3. 6 identical boxes and a 3 kg weight balance 63 kg altogether. What is the mass of 1 box?
6 · 3 kg · 63 kg · 1 · Balance scale puzzles
4. 6 identical boxes and a 5 kg weight balance 41 kg altogether. What is the mass of 1 box?
6 · 5 kg · 41 kg · 1 · Balance scale puzzles
5. 5 identical boxes and a 1 kg weight balance 31 kg altogether. What is the mass of 1 box?
5 · 1 kg · 31 kg · 1 · Balance scale puzzles
6. 2 identical boxes and a 10 kg weight balance 20 kg altogether. What is the mass of 1 box?
2 · 10 kg · 20 kg · 1 · Balance scale puzzles
7. 6 identical boxes and a 10 kg weight balance 22 kg altogether. What is the mass of 1 box?
6 · 10 kg · 22 kg · 1 · Balance scale puzzles
8. 2 identical boxes and a 3 kg weight balance 15 kg altogether. What is the mass of 1 box?
2 · 3 kg · 15 kg · 1 · Balance scale puzzles
9. 3 identical boxes and a 1 kg weight balance 31 kg altogether. What is the mass of 1 box?
3 · 1 kg · 31 kg · 1 · Balance scale puzzles
10. 2 identical boxes and a 7 kg weight balance 33 kg altogether. What is the mass of 1 box?
2 · 7 kg · 33 kg · 1 · Balance scale puzzles
11. 6 identical boxes and a 1 kg weight balance 19 kg altogether. What is the mass of 1 box?
6 · 1 kg · 19 kg · 1 · Balance scale puzzles
12. 3 identical boxes and a 12 kg weight balance 30 kg altogether. What is the mass of 1 box?
3 · 12 kg · 30 kg · 1 · Balance scale puzzles

12 questions · Seed 104730 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Balance scale puzzles

Answers and reasoning. Review before teaching.

1. 4 identical boxes and a 7 kg weight balance 23 kg altogether. What is the mass of 1 box?
4 kg
Subtract 7 kg from 23 kg to get 16 kg for 4 boxes. Divide by 4: 4 kg per box.
2. 3 identical boxes and a 3 kg weight balance 18 kg altogether. What is the mass of 1 box?
5 kg
Subtract 3 kg from 18 kg to get 15 kg for 3 boxes. Divide by 3: 5 kg per box.
3. 6 identical boxes and a 3 kg weight balance 63 kg altogether. What is the mass of 1 box?
10 kg
Subtract 3 kg from 63 kg to get 60 kg for 6 boxes. Divide by 6: 10 kg per box.
4. 6 identical boxes and a 5 kg weight balance 41 kg altogether. What is the mass of 1 box?
6 kg
Subtract 5 kg from 41 kg to get 36 kg for 6 boxes. Divide by 6: 6 kg per box.
5. 5 identical boxes and a 1 kg weight balance 31 kg altogether. What is the mass of 1 box?
6 kg
Subtract 1 kg from 31 kg to get 30 kg for 5 boxes. Divide by 5: 6 kg per box.
6. 2 identical boxes and a 10 kg weight balance 20 kg altogether. What is the mass of 1 box?
5 kg
Subtract 10 kg from 20 kg to get 10 kg for 2 boxes. Divide by 2: 5 kg per box.
7. 6 identical boxes and a 10 kg weight balance 22 kg altogether. What is the mass of 1 box?
2 kg
Subtract 10 kg from 22 kg to get 12 kg for 6 boxes. Divide by 6: 2 kg per box.
8. 2 identical boxes and a 3 kg weight balance 15 kg altogether. What is the mass of 1 box?
6 kg
Subtract 3 kg from 15 kg to get 12 kg for 2 boxes. Divide by 2: 6 kg per box.
9. 3 identical boxes and a 1 kg weight balance 31 kg altogether. What is the mass of 1 box?
10 kg
Subtract 1 kg from 31 kg to get 30 kg for 3 boxes. Divide by 3: 10 kg per box.
10. 2 identical boxes and a 7 kg weight balance 33 kg altogether. What is the mass of 1 box?
13 kg
Subtract 7 kg from 33 kg to get 26 kg for 2 boxes. Divide by 2: 13 kg per box.
11. 6 identical boxes and a 1 kg weight balance 19 kg altogether. What is the mass of 1 box?
3 kg
Subtract 1 kg from 19 kg to get 18 kg for 6 boxes. Divide by 6: 3 kg per box.
12. 3 identical boxes and a 12 kg weight balance 30 kg altogether. What is the mass of 1 box?
6 kg
Subtract 12 kg from 30 kg to get 18 kg for 3 boxes. Divide by 3: 6 kg per box.

12 questions · Seed 104730 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Balance scale puzzles

Take your time. Show your thinking.

1. 4 identical boxes and a 7 kg weight balance 23 kg altogether. What is the mass of 1 box?
4 · 7 kg · 23 kg · 1 · Balance scale puzzles
2. 3 identical boxes and a 3 kg weight balance 18 kg altogether. What is the mass of 1 box?
3 · 3 kg · 18 kg · 1 · Balance scale puzzles
3. 6 identical boxes and a 3 kg weight balance 63 kg altogether. What is the mass of 1 box?
6 · 3 kg · 63 kg · 1 · Balance scale puzzles
4. 6 identical boxes and a 5 kg weight balance 41 kg altogether. What is the mass of 1 box?
6 · 5 kg · 41 kg · 1 · Balance scale puzzles
5. 5 identical boxes and a 1 kg weight balance 31 kg altogether. What is the mass of 1 box?
5 · 1 kg · 31 kg · 1 · Balance scale puzzles
6. 2 identical boxes and a 10 kg weight balance 20 kg altogether. What is the mass of 1 box?
2 · 10 kg · 20 kg · 1 · Balance scale puzzles
7. 6 identical boxes and a 10 kg weight balance 22 kg altogether. What is the mass of 1 box?
6 · 10 kg · 22 kg · 1 · Balance scale puzzles
8. 2 identical boxes and a 3 kg weight balance 15 kg altogether. What is the mass of 1 box?
2 · 3 kg · 15 kg · 1 · Balance scale puzzles
9. 3 identical boxes and a 1 kg weight balance 31 kg altogether. What is the mass of 1 box?
3 · 1 kg · 31 kg · 1 · Balance scale puzzles
10. 2 identical boxes and a 7 kg weight balance 33 kg altogether. What is the mass of 1 box?
2 · 7 kg · 33 kg · 1 · Balance scale puzzles
11. 6 identical boxes and a 1 kg weight balance 19 kg altogether. What is the mass of 1 box?
6 · 1 kg · 19 kg · 1 · Balance scale puzzles
12. 3 identical boxes and a 12 kg weight balance 30 kg altogether. What is the mass of 1 box?
3 · 12 kg · 30 kg · 1 · Balance scale puzzles

12 questions · Seed 104730 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Balance scale puzzles

Answers and reasoning. Review before teaching.

1. 4 identical boxes and a 7 kg weight balance 23 kg altogether. What is the mass of 1 box?
4 kg
Subtract 7 kg from 23 kg to get 16 kg for 4 boxes. Divide by 4: 4 kg per box.
2. 3 identical boxes and a 3 kg weight balance 18 kg altogether. What is the mass of 1 box?
5 kg
Subtract 3 kg from 18 kg to get 15 kg for 3 boxes. Divide by 3: 5 kg per box.
3. 6 identical boxes and a 3 kg weight balance 63 kg altogether. What is the mass of 1 box?
10 kg
Subtract 3 kg from 63 kg to get 60 kg for 6 boxes. Divide by 6: 10 kg per box.
4. 6 identical boxes and a 5 kg weight balance 41 kg altogether. What is the mass of 1 box?
6 kg
Subtract 5 kg from 41 kg to get 36 kg for 6 boxes. Divide by 6: 6 kg per box.
5. 5 identical boxes and a 1 kg weight balance 31 kg altogether. What is the mass of 1 box?
6 kg
Subtract 1 kg from 31 kg to get 30 kg for 5 boxes. Divide by 5: 6 kg per box.
6. 2 identical boxes and a 10 kg weight balance 20 kg altogether. What is the mass of 1 box?
5 kg
Subtract 10 kg from 20 kg to get 10 kg for 2 boxes. Divide by 2: 5 kg per box.
7. 6 identical boxes and a 10 kg weight balance 22 kg altogether. What is the mass of 1 box?
2 kg
Subtract 10 kg from 22 kg to get 12 kg for 6 boxes. Divide by 6: 2 kg per box.
8. 2 identical boxes and a 3 kg weight balance 15 kg altogether. What is the mass of 1 box?
6 kg
Subtract 3 kg from 15 kg to get 12 kg for 2 boxes. Divide by 2: 6 kg per box.
9. 3 identical boxes and a 1 kg weight balance 31 kg altogether. What is the mass of 1 box?
10 kg
Subtract 1 kg from 31 kg to get 30 kg for 3 boxes. Divide by 3: 10 kg per box.
10. 2 identical boxes and a 7 kg weight balance 33 kg altogether. What is the mass of 1 box?
13 kg
Subtract 7 kg from 33 kg to get 26 kg for 2 boxes. Divide by 2: 13 kg per box.
11. 6 identical boxes and a 1 kg weight balance 19 kg altogether. What is the mass of 1 box?
3 kg
Subtract 1 kg from 19 kg to get 18 kg for 6 boxes. Divide by 6: 3 kg per box.
12. 3 identical boxes and a 12 kg weight balance 30 kg altogether. What is the mass of 1 box?
6 kg
Subtract 12 kg from 30 kg to get 18 kg for 3 boxes. Divide by 3: 6 kg per box.

12 questions · Seed 104730 · Age guidance, not curriculum certification