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 = 61, what number does ★ stand for?
3 · 16 · 61 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 20 = 41, what number does ★ stand for?
7 · 20 · 41 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 6 = 61, what number does ★ stand for?
5 · 6 · 61 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 9 = 34, what number does ★ stand for?
5 · 9 · 34 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 17 = 27, what number does ★ stand for?
2 · 17 · 27 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 8 = 38, what number does ★ stand for?
5 · 8 · 38 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 9 = 45, what number does ★ stand for?
6 · 9 · 45 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 13 = 22, what number does ★ stand for?
3 · 13 · 22 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 10 = 62, what number does ★ stand for?
4 · 10 · 62 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 15 = 59, what number does ★ stand for?
4 · 15 · 59 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 13 = 37, what number does ★ stand for?
2 · 13 · 37 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 4 × ★ + 1 = 9, what number does ★ stand for?
4 · 1 · 9 · Symbol equation puzzles

12 questions · Seed 104729 · 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 = 61, what number does ★ stand for?
15
Subtract 16 from 61 to get 45, then divide by 3: ★ = 15.
2. If ★ represents the same whole number each time and 7 × ★ + 20 = 41, what number does ★ stand for?
3
Subtract 20 from 41 to get 21, then divide by 7: ★ = 3.
3. If ★ represents the same whole number each time and 5 × ★ + 6 = 61, what number does ★ stand for?
11
Subtract 6 from 61 to get 55, then divide by 5: ★ = 11.
4. If ★ represents the same whole number each time and 5 × ★ + 9 = 34, what number does ★ stand for?
5
Subtract 9 from 34 to get 25, then divide by 5: ★ = 5.
5. If ★ represents the same whole number each time and 2 × ★ + 17 = 27, what number does ★ stand for?
5
Subtract 17 from 27 to get 10, then divide by 2: ★ = 5.
6. If ★ represents the same whole number each time and 5 × ★ + 8 = 38, what number does ★ stand for?
6
Subtract 8 from 38 to get 30, then divide by 5: ★ = 6.
7. If ★ represents the same whole number each time and 6 × ★ + 9 = 45, what number does ★ stand for?
6
Subtract 9 from 45 to get 36, then divide by 6: ★ = 6.
8. If ★ represents the same whole number each time and 3 × ★ + 13 = 22, what number does ★ stand for?
3
Subtract 13 from 22 to get 9, then divide by 3: ★ = 3.
9. If ★ represents the same whole number each time and 4 × ★ + 10 = 62, what number does ★ stand for?
13
Subtract 10 from 62 to get 52, then divide by 4: ★ = 13.
10. If ★ represents the same whole number each time and 4 × ★ + 15 = 59, what number does ★ stand for?
11
Subtract 15 from 59 to get 44, then divide by 4: ★ = 11.
11. If ★ represents the same whole number each time and 2 × ★ + 13 = 37, what number does ★ stand for?
12
Subtract 13 from 37 to get 24, then divide by 2: ★ = 12.
12. If ★ represents the same whole number each time and 4 × ★ + 1 = 9, what number does ★ stand for?
2
Subtract 1 from 9 to get 8, then divide by 4: ★ = 2.

12 questions · Seed 104729 · 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 = 61, what number does ★ stand for?
3 · 16 · 61 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 7 × ★ + 20 = 41, what number does ★ stand for?
7 · 20 · 41 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 5 × ★ + 6 = 61, what number does ★ stand for?
5 · 6 · 61 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 9 = 34, what number does ★ stand for?
5 · 9 · 34 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 2 × ★ + 17 = 27, what number does ★ stand for?
2 · 17 · 27 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 8 = 38, what number does ★ stand for?
5 · 8 · 38 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 9 = 45, what number does ★ stand for?
6 · 9 · 45 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 13 = 22, what number does ★ stand for?
3 · 13 · 22 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 10 = 62, what number does ★ stand for?
4 · 10 · 62 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 4 × ★ + 15 = 59, what number does ★ stand for?
4 · 15 · 59 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 13 = 37, what number does ★ stand for?
2 · 13 · 37 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 4 × ★ + 1 = 9, what number does ★ stand for?
4 · 1 · 9 · Symbol equation puzzles

12 questions · Seed 104729 · 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 = 61, what number does ★ stand for?
15
Subtract 16 from 61 to get 45, then divide by 3: ★ = 15.
2. If ★ represents the same whole number each time and 7 × ★ + 20 = 41, what number does ★ stand for?
3
Subtract 20 from 41 to get 21, then divide by 7: ★ = 3.
3. If ★ represents the same whole number each time and 5 × ★ + 6 = 61, what number does ★ stand for?
11
Subtract 6 from 61 to get 55, then divide by 5: ★ = 11.
4. If ★ represents the same whole number each time and 5 × ★ + 9 = 34, what number does ★ stand for?
5
Subtract 9 from 34 to get 25, then divide by 5: ★ = 5.
5. If ★ represents the same whole number each time and 2 × ★ + 17 = 27, what number does ★ stand for?
5
Subtract 17 from 27 to get 10, then divide by 2: ★ = 5.
6. If ★ represents the same whole number each time and 5 × ★ + 8 = 38, what number does ★ stand for?
6
Subtract 8 from 38 to get 30, then divide by 5: ★ = 6.
7. If ★ represents the same whole number each time and 6 × ★ + 9 = 45, what number does ★ stand for?
6
Subtract 9 from 45 to get 36, then divide by 6: ★ = 6.
8. If ★ represents the same whole number each time and 3 × ★ + 13 = 22, what number does ★ stand for?
3
Subtract 13 from 22 to get 9, then divide by 3: ★ = 3.
9. If ★ represents the same whole number each time and 4 × ★ + 10 = 62, what number does ★ stand for?
13
Subtract 10 from 62 to get 52, then divide by 4: ★ = 13.
10. If ★ represents the same whole number each time and 4 × ★ + 15 = 59, what number does ★ stand for?
11
Subtract 15 from 59 to get 44, then divide by 4: ★ = 11.
11. If ★ represents the same whole number each time and 2 × ★ + 13 = 37, what number does ★ stand for?
12
Subtract 13 from 37 to get 24, then divide by 2: ★ = 12.
12. If ★ represents the same whole number each time and 4 × ★ + 1 = 9, what number does ★ stand for?
2
Subtract 1 from 9 to get 8, then divide by 4: ★ = 2.

12 questions · Seed 104729 · Age guidance, not curriculum certification