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 × ★ + 13 = 49, what number does ★ stand for?
3 · 13 · 49 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 20 = 53, what number does ★ stand for?
3 · 20 · 53 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 6 × ★ + 16 = 94, what number does ★ stand for?
6 · 16 · 94 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 11 = 101, what number does ★ stand for?
6 · 11 · 101 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 6 = 38, what number does ★ stand for?
8 · 6 · 38 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 17 = 37, what number does ★ stand for?
5 · 17 · 37 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 3 × ★ + 1 = 37, what number does ★ stand for?
3 · 1 · 37 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 7 = 19, what number does ★ stand for?
3 · 7 · 19 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 8 × ★ + 4 = 60, what number does ★ stand for?
8 · 4 · 60 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 6 = 54, what number does ★ stand for?
8 · 6 · 54 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 10 = 49, what number does ★ stand for?
3 · 10 · 49 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 8 × ★ + 17 = 49, what number does ★ stand for?
8 · 17 · 49 · Symbol equation puzzles

12 questions · Seed 104734 · 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 × ★ + 13 = 49, what number does ★ stand for?
12
Subtract 13 from 49 to get 36, then divide by 3: ★ = 12.
2. If ★ represents the same whole number each time and 3 × ★ + 20 = 53, what number does ★ stand for?
11
Subtract 20 from 53 to get 33, then divide by 3: ★ = 11.
3. If ★ represents the same whole number each time and 6 × ★ + 16 = 94, what number does ★ stand for?
13
Subtract 16 from 94 to get 78, then divide by 6: ★ = 13.
4. If ★ represents the same whole number each time and 6 × ★ + 11 = 101, what number does ★ stand for?
15
Subtract 11 from 101 to get 90, then divide by 6: ★ = 15.
5. If ★ represents the same whole number each time and 8 × ★ + 6 = 38, what number does ★ stand for?
4
Subtract 6 from 38 to get 32, then divide by 8: ★ = 4.
6. If ★ represents the same whole number each time and 5 × ★ + 17 = 37, what number does ★ stand for?
4
Subtract 17 from 37 to get 20, then divide by 5: ★ = 4.
7. If ★ represents the same whole number each time and 3 × ★ + 1 = 37, what number does ★ stand for?
12
Subtract 1 from 37 to get 36, then divide by 3: ★ = 12.
8. If ★ represents the same whole number each time and 3 × ★ + 7 = 19, what number does ★ stand for?
4
Subtract 7 from 19 to get 12, then divide by 3: ★ = 4.
9. If ★ represents the same whole number each time and 8 × ★ + 4 = 60, what number does ★ stand for?
7
Subtract 4 from 60 to get 56, then divide by 8: ★ = 7.
10. If ★ represents the same whole number each time and 8 × ★ + 6 = 54, what number does ★ stand for?
6
Subtract 6 from 54 to get 48, then divide by 8: ★ = 6.
11. If ★ represents the same whole number each time and 3 × ★ + 10 = 49, what number does ★ stand for?
13
Subtract 10 from 49 to get 39, then divide by 3: ★ = 13.
12. If ★ represents the same whole number each time and 8 × ★ + 17 = 49, what number does ★ stand for?
4
Subtract 17 from 49 to get 32, then divide by 8: ★ = 4.

12 questions · Seed 104734 · 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 × ★ + 13 = 49, what number does ★ stand for?
3 · 13 · 49 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 20 = 53, what number does ★ stand for?
3 · 20 · 53 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 6 × ★ + 16 = 94, what number does ★ stand for?
6 · 16 · 94 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 11 = 101, what number does ★ stand for?
6 · 11 · 101 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 8 × ★ + 6 = 38, what number does ★ stand for?
8 · 6 · 38 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 17 = 37, what number does ★ stand for?
5 · 17 · 37 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 3 × ★ + 1 = 37, what number does ★ stand for?
3 · 1 · 37 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 7 = 19, what number does ★ stand for?
3 · 7 · 19 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 8 × ★ + 4 = 60, what number does ★ stand for?
8 · 4 · 60 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 6 = 54, what number does ★ stand for?
8 · 6 · 54 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 10 = 49, what number does ★ stand for?
3 · 10 · 49 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 8 × ★ + 17 = 49, what number does ★ stand for?
8 · 17 · 49 · Symbol equation puzzles

12 questions · Seed 104734 · 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 × ★ + 13 = 49, what number does ★ stand for?
12
Subtract 13 from 49 to get 36, then divide by 3: ★ = 12.
2. If ★ represents the same whole number each time and 3 × ★ + 20 = 53, what number does ★ stand for?
11
Subtract 20 from 53 to get 33, then divide by 3: ★ = 11.
3. If ★ represents the same whole number each time and 6 × ★ + 16 = 94, what number does ★ stand for?
13
Subtract 16 from 94 to get 78, then divide by 6: ★ = 13.
4. If ★ represents the same whole number each time and 6 × ★ + 11 = 101, what number does ★ stand for?
15
Subtract 11 from 101 to get 90, then divide by 6: ★ = 15.
5. If ★ represents the same whole number each time and 8 × ★ + 6 = 38, what number does ★ stand for?
4
Subtract 6 from 38 to get 32, then divide by 8: ★ = 4.
6. If ★ represents the same whole number each time and 5 × ★ + 17 = 37, what number does ★ stand for?
4
Subtract 17 from 37 to get 20, then divide by 5: ★ = 4.
7. If ★ represents the same whole number each time and 3 × ★ + 1 = 37, what number does ★ stand for?
12
Subtract 1 from 37 to get 36, then divide by 3: ★ = 12.
8. If ★ represents the same whole number each time and 3 × ★ + 7 = 19, what number does ★ stand for?
4
Subtract 7 from 19 to get 12, then divide by 3: ★ = 4.
9. If ★ represents the same whole number each time and 8 × ★ + 4 = 60, what number does ★ stand for?
7
Subtract 4 from 60 to get 56, then divide by 8: ★ = 7.
10. If ★ represents the same whole number each time and 8 × ★ + 6 = 54, what number does ★ stand for?
6
Subtract 6 from 54 to get 48, then divide by 8: ★ = 6.
11. If ★ represents the same whole number each time and 3 × ★ + 10 = 49, what number does ★ stand for?
13
Subtract 10 from 49 to get 39, then divide by 3: ★ = 13.
12. If ★ represents the same whole number each time and 8 × ★ + 17 = 49, what number does ★ stand for?
4
Subtract 17 from 49 to get 32, then divide by 8: ★ = 4.

12 questions · Seed 104734 · Age guidance, not curriculum certification