ReasoningAges 10-12

Symbol equation puzzles

Deduce the value of a repeated mystery symbol in a two-step arithmetic equation. 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 10-12

Symbol equation puzzles

Take your time. Show your thinking.

1. If ★ represents the same whole number each time and 3 × ★ + 16 = 58, what number does ★ stand for?
3 · 16 · 58 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 8 × ★ + 6 = 126, what number does ★ stand for?
8 · 6 · 126 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 4 = 14, what number does ★ stand for?
5 · 4 · 14 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 12 = 28, what number does ★ stand for?
8 · 12 · 28 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 8 = 80, what number does ★ stand for?
8 · 8 · 80 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 9 = 65, what number does ★ stand for?
7 · 9 · 65 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 1 = 17, what number does ★ stand for?
4 · 1 · 17 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 6 × ★ + 18 = 30, what number does ★ stand for?
6 · 18 · 30 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 8 × ★ + 9 = 57, what number does ★ stand for?
8 · 9 · 57 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 4 = 40, what number does ★ stand for?
3 · 4 · 40 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 5 = 37, what number does ★ stand for?
8 · 5 · 37 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 3 = 38, what number does ★ stand for?
7 · 3 · 38 · Symbol equation puzzles

12 questions · Seed 104739 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Symbol equation puzzles

Answers and reasoning. Review before teaching.

1. If ★ represents the same whole number each time and 3 × ★ + 16 = 58, what number does ★ stand for?
14
Subtract 16 from 58 to get 42, then divide by 3: ★ = 14.
2. If ★ represents the same whole number each time and 8 × ★ + 6 = 126, what number does ★ stand for?
15
Subtract 6 from 126 to get 120, then divide by 8: ★ = 15.
3. If ★ represents the same whole number each time and 5 × ★ + 4 = 14, what number does ★ stand for?
2
Subtract 4 from 14 to get 10, then divide by 5: ★ = 2.
4. If ★ represents the same whole number each time and 8 × ★ + 12 = 28, what number does ★ stand for?
2
Subtract 12 from 28 to get 16, then divide by 8: ★ = 2.
5. If ★ represents the same whole number each time and 8 × ★ + 8 = 80, what number does ★ stand for?
9
Subtract 8 from 80 to get 72, then divide by 8: ★ = 9.
6. If ★ represents the same whole number each time and 7 × ★ + 9 = 65, what number does ★ stand for?
8
Subtract 9 from 65 to get 56, then divide by 7: ★ = 8.
7. If ★ represents the same whole number each time and 4 × ★ + 1 = 17, what number does ★ stand for?
4
Subtract 1 from 17 to get 16, then divide by 4: ★ = 4.
8. If ★ represents the same whole number each time and 6 × ★ + 18 = 30, what number does ★ stand for?
2
Subtract 18 from 30 to get 12, then divide by 6: ★ = 2.
9. If ★ represents the same whole number each time and 8 × ★ + 9 = 57, what number does ★ stand for?
6
Subtract 9 from 57 to get 48, then divide by 8: ★ = 6.
10. If ★ represents the same whole number each time and 3 × ★ + 4 = 40, what number does ★ stand for?
12
Subtract 4 from 40 to get 36, then divide by 3: ★ = 12.
11. If ★ represents the same whole number each time and 8 × ★ + 5 = 37, what number does ★ stand for?
4
Subtract 5 from 37 to get 32, then divide by 8: ★ = 4.
12. If ★ represents the same whole number each time and 7 × ★ + 3 = 38, what number does ★ stand for?
5
Subtract 3 from 38 to get 35, then divide by 7: ★ = 5.

12 questions · Seed 104739 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Symbol equation puzzles

Take your time. Show your thinking.

1. If ★ represents the same whole number each time and 3 × ★ + 16 = 58, what number does ★ stand for?
3 · 16 · 58 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 8 × ★ + 6 = 126, what number does ★ stand for?
8 · 6 · 126 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 4 = 14, what number does ★ stand for?
5 · 4 · 14 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 12 = 28, what number does ★ stand for?
8 · 12 · 28 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 8 = 80, what number does ★ stand for?
8 · 8 · 80 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 9 = 65, what number does ★ stand for?
7 · 9 · 65 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 1 = 17, what number does ★ stand for?
4 · 1 · 17 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 6 × ★ + 18 = 30, what number does ★ stand for?
6 · 18 · 30 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 8 × ★ + 9 = 57, what number does ★ stand for?
8 · 9 · 57 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 4 = 40, what number does ★ stand for?
3 · 4 · 40 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 5 = 37, what number does ★ stand for?
8 · 5 · 37 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 3 = 38, what number does ★ stand for?
7 · 3 · 38 · Symbol equation puzzles

12 questions · Seed 104739 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Symbol equation puzzles

Answers and reasoning. Review before teaching.

1. If ★ represents the same whole number each time and 3 × ★ + 16 = 58, what number does ★ stand for?
14
Subtract 16 from 58 to get 42, then divide by 3: ★ = 14.
2. If ★ represents the same whole number each time and 8 × ★ + 6 = 126, what number does ★ stand for?
15
Subtract 6 from 126 to get 120, then divide by 8: ★ = 15.
3. If ★ represents the same whole number each time and 5 × ★ + 4 = 14, what number does ★ stand for?
2
Subtract 4 from 14 to get 10, then divide by 5: ★ = 2.
4. If ★ represents the same whole number each time and 8 × ★ + 12 = 28, what number does ★ stand for?
2
Subtract 12 from 28 to get 16, then divide by 8: ★ = 2.
5. If ★ represents the same whole number each time and 8 × ★ + 8 = 80, what number does ★ stand for?
9
Subtract 8 from 80 to get 72, then divide by 8: ★ = 9.
6. If ★ represents the same whole number each time and 7 × ★ + 9 = 65, what number does ★ stand for?
8
Subtract 9 from 65 to get 56, then divide by 7: ★ = 8.
7. If ★ represents the same whole number each time and 4 × ★ + 1 = 17, what number does ★ stand for?
4
Subtract 1 from 17 to get 16, then divide by 4: ★ = 4.
8. If ★ represents the same whole number each time and 6 × ★ + 18 = 30, what number does ★ stand for?
2
Subtract 18 from 30 to get 12, then divide by 6: ★ = 2.
9. If ★ represents the same whole number each time and 8 × ★ + 9 = 57, what number does ★ stand for?
6
Subtract 9 from 57 to get 48, then divide by 8: ★ = 6.
10. If ★ represents the same whole number each time and 3 × ★ + 4 = 40, what number does ★ stand for?
12
Subtract 4 from 40 to get 36, then divide by 3: ★ = 12.
11. If ★ represents the same whole number each time and 8 × ★ + 5 = 37, what number does ★ stand for?
4
Subtract 5 from 37 to get 32, then divide by 8: ★ = 4.
12. If ★ represents the same whole number each time and 7 × ★ + 3 = 38, what number does ★ stand for?
5
Subtract 3 from 38 to get 35, then divide by 7: ★ = 5.

12 questions · Seed 104739 · Age guidance, not curriculum certification