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 8 × ★ + 10 = 74, what number does ★ stand for?
8 · 10 · 74 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 5 = 33, what number does ★ stand for?
2 · 5 · 33 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 8 = 22, what number does ★ stand for?
7 · 8 · 22 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 10 = 66, what number does ★ stand for?
8 · 10 · 66 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 5 = 33, what number does ★ stand for?
7 · 5 · 33 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 3 = 12, what number does ★ stand for?
3 · 3 · 12 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 16 = 51, what number does ★ stand for?
5 · 16 · 51 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 9 = 69, what number does ★ stand for?
5 · 9 · 69 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 6 = 34, what number does ★ stand for?
4 · 6 · 34 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 1 = 17, what number does ★ stand for?
4 · 1 · 17 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 1 = 56, what number does ★ stand for?
5 · 1 · 56 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 12 = 42, what number does ★ stand for?
5 · 12 · 42 · Symbol equation puzzles

12 questions · Seed 86 · 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 8 × ★ + 10 = 74, what number does ★ stand for?
8
Subtract 10 from 74 to get 64, then divide by 8: ★ = 8.
2. If ★ represents the same whole number each time and 2 × ★ + 5 = 33, what number does ★ stand for?
14
Subtract 5 from 33 to get 28, then divide by 2: ★ = 14.
3. If ★ represents the same whole number each time and 7 × ★ + 8 = 22, what number does ★ stand for?
2
Subtract 8 from 22 to get 14, then divide by 7: ★ = 2.
4. If ★ represents the same whole number each time and 8 × ★ + 10 = 66, what number does ★ stand for?
7
Subtract 10 from 66 to get 56, then divide by 8: ★ = 7.
5. If ★ represents the same whole number each time and 7 × ★ + 5 = 33, what number does ★ stand for?
4
Subtract 5 from 33 to get 28, then divide by 7: ★ = 4.
6. If ★ represents the same whole number each time and 3 × ★ + 3 = 12, what number does ★ stand for?
3
Subtract 3 from 12 to get 9, then divide by 3: ★ = 3.
7. If ★ represents the same whole number each time and 5 × ★ + 16 = 51, what number does ★ stand for?
7
Subtract 16 from 51 to get 35, then divide by 5: ★ = 7.
8. If ★ represents the same whole number each time and 5 × ★ + 9 = 69, what number does ★ stand for?
12
Subtract 9 from 69 to get 60, then divide by 5: ★ = 12.
9. If ★ represents the same whole number each time and 4 × ★ + 6 = 34, what number does ★ stand for?
7
Subtract 6 from 34 to get 28, then divide by 4: ★ = 7.
10. 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.
11. If ★ represents the same whole number each time and 5 × ★ + 1 = 56, what number does ★ stand for?
11
Subtract 1 from 56 to get 55, then divide by 5: ★ = 11.
12. If ★ represents the same whole number each time and 5 × ★ + 12 = 42, what number does ★ stand for?
6
Subtract 12 from 42 to get 30, then divide by 5: ★ = 6.

12 questions · Seed 86 · 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 8 × ★ + 10 = 74, what number does ★ stand for?
8 · 10 · 74 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 2 × ★ + 5 = 33, what number does ★ stand for?
2 · 5 · 33 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 7 × ★ + 8 = 22, what number does ★ stand for?
7 · 8 · 22 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 10 = 66, what number does ★ stand for?
8 · 10 · 66 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 5 = 33, what number does ★ stand for?
7 · 5 · 33 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 3 = 12, what number does ★ stand for?
3 · 3 · 12 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 16 = 51, what number does ★ stand for?
5 · 16 · 51 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 5 × ★ + 9 = 69, what number does ★ stand for?
5 · 9 · 69 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 6 = 34, what number does ★ stand for?
4 · 6 · 34 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 1 = 17, what number does ★ stand for?
4 · 1 · 17 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 5 × ★ + 1 = 56, what number does ★ stand for?
5 · 1 · 56 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 12 = 42, what number does ★ stand for?
5 · 12 · 42 · Symbol equation puzzles

12 questions · Seed 86 · 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 8 × ★ + 10 = 74, what number does ★ stand for?
8
Subtract 10 from 74 to get 64, then divide by 8: ★ = 8.
2. If ★ represents the same whole number each time and 2 × ★ + 5 = 33, what number does ★ stand for?
14
Subtract 5 from 33 to get 28, then divide by 2: ★ = 14.
3. If ★ represents the same whole number each time and 7 × ★ + 8 = 22, what number does ★ stand for?
2
Subtract 8 from 22 to get 14, then divide by 7: ★ = 2.
4. If ★ represents the same whole number each time and 8 × ★ + 10 = 66, what number does ★ stand for?
7
Subtract 10 from 66 to get 56, then divide by 8: ★ = 7.
5. If ★ represents the same whole number each time and 7 × ★ + 5 = 33, what number does ★ stand for?
4
Subtract 5 from 33 to get 28, then divide by 7: ★ = 4.
6. If ★ represents the same whole number each time and 3 × ★ + 3 = 12, what number does ★ stand for?
3
Subtract 3 from 12 to get 9, then divide by 3: ★ = 3.
7. If ★ represents the same whole number each time and 5 × ★ + 16 = 51, what number does ★ stand for?
7
Subtract 16 from 51 to get 35, then divide by 5: ★ = 7.
8. If ★ represents the same whole number each time and 5 × ★ + 9 = 69, what number does ★ stand for?
12
Subtract 9 from 69 to get 60, then divide by 5: ★ = 12.
9. If ★ represents the same whole number each time and 4 × ★ + 6 = 34, what number does ★ stand for?
7
Subtract 6 from 34 to get 28, then divide by 4: ★ = 7.
10. 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.
11. If ★ represents the same whole number each time and 5 × ★ + 1 = 56, what number does ★ stand for?
11
Subtract 1 from 56 to get 55, then divide by 5: ★ = 11.
12. If ★ represents the same whole number each time and 5 × ★ + 12 = 42, what number does ★ stand for?
6
Subtract 12 from 42 to get 30, then divide by 5: ★ = 6.

12 questions · Seed 86 · Age guidance, not curriculum certification