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 7 × ★ + 12 = 89, what number does ★ stand for?
7 · 12 · 89 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 18 = 60, what number does ★ stand for?
6 · 18 · 60 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 9 = 45, what number does ★ stand for?
4 · 9 · 45 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 7 × ★ + 3 = 31, what number does ★ stand for?
7 · 3 · 31 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 2 = 86, what number does ★ stand for?
6 · 2 · 86 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 5 = 15, what number does ★ stand for?
5 · 5 · 15 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 18 = 50, what number does ★ stand for?
4 · 18 · 50 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 2 × ★ + 17 = 39, what number does ★ stand for?
2 · 17 · 39 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 13 = 33, what number does ★ stand for?
5 · 13 · 33 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 8 = 12, what number does ★ stand for?
2 · 8 · 12 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 19 = 35, what number does ★ stand for?
8 · 19 · 35 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 2 × ★ + 12 = 20, what number does ★ stand for?
2 · 12 · 20 · Symbol equation puzzles

12 questions · Seed 104732 · 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 7 × ★ + 12 = 89, what number does ★ stand for?
11
Subtract 12 from 89 to get 77, then divide by 7: ★ = 11.
2. If ★ represents the same whole number each time and 6 × ★ + 18 = 60, what number does ★ stand for?
7
Subtract 18 from 60 to get 42, then divide by 6: ★ = 7.
3. If ★ represents the same whole number each time and 4 × ★ + 9 = 45, what number does ★ stand for?
9
Subtract 9 from 45 to get 36, then divide by 4: ★ = 9.
4. If ★ represents the same whole number each time and 7 × ★ + 3 = 31, what number does ★ stand for?
4
Subtract 3 from 31 to get 28, then divide by 7: ★ = 4.
5. If ★ represents the same whole number each time and 6 × ★ + 2 = 86, what number does ★ stand for?
14
Subtract 2 from 86 to get 84, then divide by 6: ★ = 14.
6. If ★ represents the same whole number each time and 5 × ★ + 5 = 15, what number does ★ stand for?
2
Subtract 5 from 15 to get 10, then divide by 5: ★ = 2.
7. If ★ represents the same whole number each time and 4 × ★ + 18 = 50, what number does ★ stand for?
8
Subtract 18 from 50 to get 32, then divide by 4: ★ = 8.
8. If ★ represents the same whole number each time and 2 × ★ + 17 = 39, what number does ★ stand for?
11
Subtract 17 from 39 to get 22, then divide by 2: ★ = 11.
9. If ★ represents the same whole number each time and 5 × ★ + 13 = 33, what number does ★ stand for?
4
Subtract 13 from 33 to get 20, then divide by 5: ★ = 4.
10. If ★ represents the same whole number each time and 2 × ★ + 8 = 12, what number does ★ stand for?
2
Subtract 8 from 12 to get 4, then divide by 2: ★ = 2.
11. If ★ represents the same whole number each time and 8 × ★ + 19 = 35, what number does ★ stand for?
2
Subtract 19 from 35 to get 16, then divide by 8: ★ = 2.
12. If ★ represents the same whole number each time and 2 × ★ + 12 = 20, what number does ★ stand for?
4
Subtract 12 from 20 to get 8, then divide by 2: ★ = 4.

12 questions · Seed 104732 · 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 7 × ★ + 12 = 89, what number does ★ stand for?
7 · 12 · 89 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 18 = 60, what number does ★ stand for?
6 · 18 · 60 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 9 = 45, what number does ★ stand for?
4 · 9 · 45 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 7 × ★ + 3 = 31, what number does ★ stand for?
7 · 3 · 31 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 6 × ★ + 2 = 86, what number does ★ stand for?
6 · 2 · 86 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 5 = 15, what number does ★ stand for?
5 · 5 · 15 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 18 = 50, what number does ★ stand for?
4 · 18 · 50 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 2 × ★ + 17 = 39, what number does ★ stand for?
2 · 17 · 39 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 13 = 33, what number does ★ stand for?
5 · 13 · 33 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 2 × ★ + 8 = 12, what number does ★ stand for?
2 · 8 · 12 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 8 × ★ + 19 = 35, what number does ★ stand for?
8 · 19 · 35 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 2 × ★ + 12 = 20, what number does ★ stand for?
2 · 12 · 20 · Symbol equation puzzles

12 questions · Seed 104732 · 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 7 × ★ + 12 = 89, what number does ★ stand for?
11
Subtract 12 from 89 to get 77, then divide by 7: ★ = 11.
2. If ★ represents the same whole number each time and 6 × ★ + 18 = 60, what number does ★ stand for?
7
Subtract 18 from 60 to get 42, then divide by 6: ★ = 7.
3. If ★ represents the same whole number each time and 4 × ★ + 9 = 45, what number does ★ stand for?
9
Subtract 9 from 45 to get 36, then divide by 4: ★ = 9.
4. If ★ represents the same whole number each time and 7 × ★ + 3 = 31, what number does ★ stand for?
4
Subtract 3 from 31 to get 28, then divide by 7: ★ = 4.
5. If ★ represents the same whole number each time and 6 × ★ + 2 = 86, what number does ★ stand for?
14
Subtract 2 from 86 to get 84, then divide by 6: ★ = 14.
6. If ★ represents the same whole number each time and 5 × ★ + 5 = 15, what number does ★ stand for?
2
Subtract 5 from 15 to get 10, then divide by 5: ★ = 2.
7. If ★ represents the same whole number each time and 4 × ★ + 18 = 50, what number does ★ stand for?
8
Subtract 18 from 50 to get 32, then divide by 4: ★ = 8.
8. If ★ represents the same whole number each time and 2 × ★ + 17 = 39, what number does ★ stand for?
11
Subtract 17 from 39 to get 22, then divide by 2: ★ = 11.
9. If ★ represents the same whole number each time and 5 × ★ + 13 = 33, what number does ★ stand for?
4
Subtract 13 from 33 to get 20, then divide by 5: ★ = 4.
10. If ★ represents the same whole number each time and 2 × ★ + 8 = 12, what number does ★ stand for?
2
Subtract 8 from 12 to get 4, then divide by 2: ★ = 2.
11. If ★ represents the same whole number each time and 8 × ★ + 19 = 35, what number does ★ stand for?
2
Subtract 19 from 35 to get 16, then divide by 8: ★ = 2.
12. If ★ represents the same whole number each time and 2 × ★ + 12 = 20, what number does ★ stand for?
4
Subtract 12 from 20 to get 8, then divide by 2: ★ = 4.

12 questions · Seed 104732 · Age guidance, not curriculum certification