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 5 × ★ + 16 = 41, what number does ★ stand for?
5 · 16 · 41 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 4 × ★ + 5 = 21, what number does ★ stand for?
4 · 5 · 21 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 14 = 42, what number does ★ stand for?
4 · 14 · 42 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 5 = 125, what number does ★ stand for?
8 · 5 · 125 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 3 = 45, what number does ★ stand for?
3 · 3 · 45 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 7 = 37, what number does ★ stand for?
3 · 7 · 37 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 1 = 73, what number does ★ stand for?
6 · 1 · 73 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 10 = 22, what number does ★ stand for?
3 · 10 · 22 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 2 = 34, what number does ★ stand for?
4 · 2 · 34 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 20 = 53, what number does ★ stand for?
3 · 20 · 53 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 19 = 41, what number does ★ stand for?
2 · 19 · 41 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 6 × ★ + 19 = 61, what number does ★ stand for?
6 · 19 · 61 · Symbol equation puzzles

12 questions · Seed 79 · 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 5 × ★ + 16 = 41, what number does ★ stand for?
5
Subtract 16 from 41 to get 25, then divide by 5: ★ = 5.
2. If ★ represents the same whole number each time and 4 × ★ + 5 = 21, what number does ★ stand for?
4
Subtract 5 from 21 to get 16, then divide by 4: ★ = 4.
3. If ★ represents the same whole number each time and 4 × ★ + 14 = 42, what number does ★ stand for?
7
Subtract 14 from 42 to get 28, then divide by 4: ★ = 7.
4. If ★ represents the same whole number each time and 8 × ★ + 5 = 125, what number does ★ stand for?
15
Subtract 5 from 125 to get 120, then divide by 8: ★ = 15.
5. If ★ represents the same whole number each time and 3 × ★ + 3 = 45, what number does ★ stand for?
14
Subtract 3 from 45 to get 42, then divide by 3: ★ = 14.
6. If ★ represents the same whole number each time and 3 × ★ + 7 = 37, what number does ★ stand for?
10
Subtract 7 from 37 to get 30, then divide by 3: ★ = 10.
7. If ★ represents the same whole number each time and 6 × ★ + 1 = 73, what number does ★ stand for?
12
Subtract 1 from 73 to get 72, then divide by 6: ★ = 12.
8. If ★ represents the same whole number each time and 3 × ★ + 10 = 22, what number does ★ stand for?
4
Subtract 10 from 22 to get 12, then divide by 3: ★ = 4.
9. If ★ represents the same whole number each time and 4 × ★ + 2 = 34, what number does ★ stand for?
8
Subtract 2 from 34 to get 32, then divide by 4: ★ = 8.
10. 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.
11. If ★ represents the same whole number each time and 2 × ★ + 19 = 41, what number does ★ stand for?
11
Subtract 19 from 41 to get 22, then divide by 2: ★ = 11.
12. If ★ represents the same whole number each time and 6 × ★ + 19 = 61, what number does ★ stand for?
7
Subtract 19 from 61 to get 42, then divide by 6: ★ = 7.

12 questions · Seed 79 · 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 5 × ★ + 16 = 41, what number does ★ stand for?
5 · 16 · 41 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 4 × ★ + 5 = 21, what number does ★ stand for?
4 · 5 · 21 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 14 = 42, what number does ★ stand for?
4 · 14 · 42 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 8 × ★ + 5 = 125, what number does ★ stand for?
8 · 5 · 125 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 3 = 45, what number does ★ stand for?
3 · 3 · 45 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 3 × ★ + 7 = 37, what number does ★ stand for?
3 · 7 · 37 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 6 × ★ + 1 = 73, what number does ★ stand for?
6 · 1 · 73 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 3 × ★ + 10 = 22, what number does ★ stand for?
3 · 10 · 22 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 4 × ★ + 2 = 34, what number does ★ stand for?
4 · 2 · 34 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 3 × ★ + 20 = 53, what number does ★ stand for?
3 · 20 · 53 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 2 × ★ + 19 = 41, what number does ★ stand for?
2 · 19 · 41 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 6 × ★ + 19 = 61, what number does ★ stand for?
6 · 19 · 61 · Symbol equation puzzles

12 questions · Seed 79 · 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 5 × ★ + 16 = 41, what number does ★ stand for?
5
Subtract 16 from 41 to get 25, then divide by 5: ★ = 5.
2. If ★ represents the same whole number each time and 4 × ★ + 5 = 21, what number does ★ stand for?
4
Subtract 5 from 21 to get 16, then divide by 4: ★ = 4.
3. If ★ represents the same whole number each time and 4 × ★ + 14 = 42, what number does ★ stand for?
7
Subtract 14 from 42 to get 28, then divide by 4: ★ = 7.
4. If ★ represents the same whole number each time and 8 × ★ + 5 = 125, what number does ★ stand for?
15
Subtract 5 from 125 to get 120, then divide by 8: ★ = 15.
5. If ★ represents the same whole number each time and 3 × ★ + 3 = 45, what number does ★ stand for?
14
Subtract 3 from 45 to get 42, then divide by 3: ★ = 14.
6. If ★ represents the same whole number each time and 3 × ★ + 7 = 37, what number does ★ stand for?
10
Subtract 7 from 37 to get 30, then divide by 3: ★ = 10.
7. If ★ represents the same whole number each time and 6 × ★ + 1 = 73, what number does ★ stand for?
12
Subtract 1 from 73 to get 72, then divide by 6: ★ = 12.
8. If ★ represents the same whole number each time and 3 × ★ + 10 = 22, what number does ★ stand for?
4
Subtract 10 from 22 to get 12, then divide by 3: ★ = 4.
9. If ★ represents the same whole number each time and 4 × ★ + 2 = 34, what number does ★ stand for?
8
Subtract 2 from 34 to get 32, then divide by 4: ★ = 8.
10. 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.
11. If ★ represents the same whole number each time and 2 × ★ + 19 = 41, what number does ★ stand for?
11
Subtract 19 from 41 to get 22, then divide by 2: ★ = 11.
12. If ★ represents the same whole number each time and 6 × ★ + 19 = 61, what number does ★ stand for?
7
Subtract 19 from 61 to get 42, then divide by 6: ★ = 7.

12 questions · Seed 79 · Age guidance, not curriculum certification