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 6 × ★ + 5 = 83, what number does ★ stand for?
6 · 5 · 83 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 12 = 102, what number does ★ stand for?
6 · 12 · 102 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 8 = 20, what number does ★ stand for?
2 · 8 · 20 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 3 = 17, what number does ★ stand for?
2 · 3 · 17 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 20 = 44, what number does ★ stand for?
8 · 20 · 44 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 5 = 47, what number does ★ stand for?
7 · 5 · 47 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 14 = 32, what number does ★ stand for?
2 · 14 · 32 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 6 × ★ + 13 = 37, what number does ★ stand for?
6 · 13 · 37 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 20 = 69, what number does ★ stand for?
7 · 20 · 69 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 8 = 16, what number does ★ stand for?
2 · 8 · 16 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 20 = 48, what number does ★ stand for?
2 · 20 · 48 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 14 = 29, what number does ★ stand for?
5 · 14 · 29 · Symbol equation puzzles

12 questions · Seed 104736 · 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 6 × ★ + 5 = 83, what number does ★ stand for?
13
Subtract 5 from 83 to get 78, then divide by 6: ★ = 13.
2. If ★ represents the same whole number each time and 6 × ★ + 12 = 102, what number does ★ stand for?
15
Subtract 12 from 102 to get 90, then divide by 6: ★ = 15.
3. If ★ represents the same whole number each time and 2 × ★ + 8 = 20, what number does ★ stand for?
6
Subtract 8 from 20 to get 12, then divide by 2: ★ = 6.
4. If ★ represents the same whole number each time and 2 × ★ + 3 = 17, what number does ★ stand for?
7
Subtract 3 from 17 to get 14, then divide by 2: ★ = 7.
5. If ★ represents the same whole number each time and 8 × ★ + 20 = 44, what number does ★ stand for?
3
Subtract 20 from 44 to get 24, then divide by 8: ★ = 3.
6. If ★ represents the same whole number each time and 7 × ★ + 5 = 47, what number does ★ stand for?
6
Subtract 5 from 47 to get 42, then divide by 7: ★ = 6.
7. If ★ represents the same whole number each time and 2 × ★ + 14 = 32, what number does ★ stand for?
9
Subtract 14 from 32 to get 18, then divide by 2: ★ = 9.
8. If ★ represents the same whole number each time and 6 × ★ + 13 = 37, what number does ★ stand for?
4
Subtract 13 from 37 to get 24, then divide by 6: ★ = 4.
9. If ★ represents the same whole number each time and 7 × ★ + 20 = 69, what number does ★ stand for?
7
Subtract 20 from 69 to get 49, then divide by 7: ★ = 7.
10. If ★ represents the same whole number each time and 2 × ★ + 8 = 16, what number does ★ stand for?
4
Subtract 8 from 16 to get 8, then divide by 2: ★ = 4.
11. If ★ represents the same whole number each time and 2 × ★ + 20 = 48, what number does ★ stand for?
14
Subtract 20 from 48 to get 28, then divide by 2: ★ = 14.
12. If ★ represents the same whole number each time and 5 × ★ + 14 = 29, what number does ★ stand for?
3
Subtract 14 from 29 to get 15, then divide by 5: ★ = 3.

12 questions · Seed 104736 · 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 6 × ★ + 5 = 83, what number does ★ stand for?
6 · 5 · 83 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 12 = 102, what number does ★ stand for?
6 · 12 · 102 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 2 × ★ + 8 = 20, what number does ★ stand for?
2 · 8 · 20 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 2 × ★ + 3 = 17, what number does ★ stand for?
2 · 3 · 17 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 20 = 44, what number does ★ stand for?
8 · 20 · 44 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 7 × ★ + 5 = 47, what number does ★ stand for?
7 · 5 · 47 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 2 × ★ + 14 = 32, what number does ★ stand for?
2 · 14 · 32 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 6 × ★ + 13 = 37, what number does ★ stand for?
6 · 13 · 37 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 7 × ★ + 20 = 69, what number does ★ stand for?
7 · 20 · 69 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 8 = 16, what number does ★ stand for?
2 · 8 · 16 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 20 = 48, what number does ★ stand for?
2 · 20 · 48 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 14 = 29, what number does ★ stand for?
5 · 14 · 29 · Symbol equation puzzles

12 questions · Seed 104736 · 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 6 × ★ + 5 = 83, what number does ★ stand for?
13
Subtract 5 from 83 to get 78, then divide by 6: ★ = 13.
2. If ★ represents the same whole number each time and 6 × ★ + 12 = 102, what number does ★ stand for?
15
Subtract 12 from 102 to get 90, then divide by 6: ★ = 15.
3. If ★ represents the same whole number each time and 2 × ★ + 8 = 20, what number does ★ stand for?
6
Subtract 8 from 20 to get 12, then divide by 2: ★ = 6.
4. If ★ represents the same whole number each time and 2 × ★ + 3 = 17, what number does ★ stand for?
7
Subtract 3 from 17 to get 14, then divide by 2: ★ = 7.
5. If ★ represents the same whole number each time and 8 × ★ + 20 = 44, what number does ★ stand for?
3
Subtract 20 from 44 to get 24, then divide by 8: ★ = 3.
6. If ★ represents the same whole number each time and 7 × ★ + 5 = 47, what number does ★ stand for?
6
Subtract 5 from 47 to get 42, then divide by 7: ★ = 6.
7. If ★ represents the same whole number each time and 2 × ★ + 14 = 32, what number does ★ stand for?
9
Subtract 14 from 32 to get 18, then divide by 2: ★ = 9.
8. If ★ represents the same whole number each time and 6 × ★ + 13 = 37, what number does ★ stand for?
4
Subtract 13 from 37 to get 24, then divide by 6: ★ = 4.
9. If ★ represents the same whole number each time and 7 × ★ + 20 = 69, what number does ★ stand for?
7
Subtract 20 from 69 to get 49, then divide by 7: ★ = 7.
10. If ★ represents the same whole number each time and 2 × ★ + 8 = 16, what number does ★ stand for?
4
Subtract 8 from 16 to get 8, then divide by 2: ★ = 4.
11. If ★ represents the same whole number each time and 2 × ★ + 20 = 48, what number does ★ stand for?
14
Subtract 20 from 48 to get 28, then divide by 2: ★ = 14.
12. If ★ represents the same whole number each time and 5 × ★ + 14 = 29, what number does ★ stand for?
3
Subtract 14 from 29 to get 15, then divide by 5: ★ = 3.

12 questions · Seed 104736 · Age guidance, not curriculum certification