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 × ★ + 20 = 90, what number does ★ stand for?
7 · 20 · 90 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 11 = 83, what number does ★ stand for?
6 · 11 · 83 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 8 × ★ + 20 = 44, what number does ★ stand for?
8 · 20 · 44 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 4 × ★ + 10 = 42, what number does ★ stand for?
4 · 10 · 42 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 17 = 31, what number does ★ stand for?
7 · 17 · 31 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 13 = 133, what number does ★ stand for?
8 · 13 · 133 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 3 × ★ + 7 = 49, what number does ★ stand for?
3 · 7 · 49 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 19 = 51, what number does ★ stand for?
8 · 19 · 51 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 6 = 51, what number does ★ stand for?
5 · 6 · 51 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 11 = 67, what number does ★ stand for?
8 · 11 · 67 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 4 × ★ + 3 = 47, what number does ★ stand for?
4 · 3 · 47 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 13 = 33, what number does ★ stand for?
5 · 13 · 33 · Symbol equation puzzles

12 questions · Seed 77 · 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 × ★ + 20 = 90, what number does ★ stand for?
10
Subtract 20 from 90 to get 70, then divide by 7: ★ = 10.
2. If ★ represents the same whole number each time and 6 × ★ + 11 = 83, what number does ★ stand for?
12
Subtract 11 from 83 to get 72, then divide by 6: ★ = 12.
3. If ★ represents the same whole number each time and 8 × ★ + 20 = 44, what number does ★ stand for?
3
Subtract 20 from 44 to get 24, then divide by 8: ★ = 3.
4. If ★ represents the same whole number each time and 4 × ★ + 10 = 42, what number does ★ stand for?
8
Subtract 10 from 42 to get 32, then divide by 4: ★ = 8.
5. If ★ represents the same whole number each time and 7 × ★ + 17 = 31, what number does ★ stand for?
2
Subtract 17 from 31 to get 14, then divide by 7: ★ = 2.
6. If ★ represents the same whole number each time and 8 × ★ + 13 = 133, what number does ★ stand for?
15
Subtract 13 from 133 to get 120, then divide by 8: ★ = 15.
7. If ★ represents the same whole number each time and 3 × ★ + 7 = 49, what number does ★ stand for?
14
Subtract 7 from 49 to get 42, then divide by 3: ★ = 14.
8. If ★ represents the same whole number each time and 8 × ★ + 19 = 51, what number does ★ stand for?
4
Subtract 19 from 51 to get 32, then divide by 8: ★ = 4.
9. If ★ represents the same whole number each time and 5 × ★ + 6 = 51, what number does ★ stand for?
9
Subtract 6 from 51 to get 45, then divide by 5: ★ = 9.
10. If ★ represents the same whole number each time and 8 × ★ + 11 = 67, what number does ★ stand for?
7
Subtract 11 from 67 to get 56, then divide by 8: ★ = 7.
11. If ★ represents the same whole number each time and 4 × ★ + 3 = 47, what number does ★ stand for?
11
Subtract 3 from 47 to get 44, then divide by 4: ★ = 11.
12. 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.

12 questions · Seed 77 · 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 × ★ + 20 = 90, what number does ★ stand for?
7 · 20 · 90 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 11 = 83, what number does ★ stand for?
6 · 11 · 83 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 8 × ★ + 20 = 44, what number does ★ stand for?
8 · 20 · 44 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 4 × ★ + 10 = 42, what number does ★ stand for?
4 · 10 · 42 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 7 × ★ + 17 = 31, what number does ★ stand for?
7 · 17 · 31 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 8 × ★ + 13 = 133, what number does ★ stand for?
8 · 13 · 133 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 3 × ★ + 7 = 49, what number does ★ stand for?
3 · 7 · 49 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 8 × ★ + 19 = 51, what number does ★ stand for?
8 · 19 · 51 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 5 × ★ + 6 = 51, what number does ★ stand for?
5 · 6 · 51 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 11 = 67, what number does ★ stand for?
8 · 11 · 67 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 4 × ★ + 3 = 47, what number does ★ stand for?
4 · 3 · 47 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 5 × ★ + 13 = 33, what number does ★ stand for?
5 · 13 · 33 · Symbol equation puzzles

12 questions · Seed 77 · 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 × ★ + 20 = 90, what number does ★ stand for?
10
Subtract 20 from 90 to get 70, then divide by 7: ★ = 10.
2. If ★ represents the same whole number each time and 6 × ★ + 11 = 83, what number does ★ stand for?
12
Subtract 11 from 83 to get 72, then divide by 6: ★ = 12.
3. If ★ represents the same whole number each time and 8 × ★ + 20 = 44, what number does ★ stand for?
3
Subtract 20 from 44 to get 24, then divide by 8: ★ = 3.
4. If ★ represents the same whole number each time and 4 × ★ + 10 = 42, what number does ★ stand for?
8
Subtract 10 from 42 to get 32, then divide by 4: ★ = 8.
5. If ★ represents the same whole number each time and 7 × ★ + 17 = 31, what number does ★ stand for?
2
Subtract 17 from 31 to get 14, then divide by 7: ★ = 2.
6. If ★ represents the same whole number each time and 8 × ★ + 13 = 133, what number does ★ stand for?
15
Subtract 13 from 133 to get 120, then divide by 8: ★ = 15.
7. If ★ represents the same whole number each time and 3 × ★ + 7 = 49, what number does ★ stand for?
14
Subtract 7 from 49 to get 42, then divide by 3: ★ = 14.
8. If ★ represents the same whole number each time and 8 × ★ + 19 = 51, what number does ★ stand for?
4
Subtract 19 from 51 to get 32, then divide by 8: ★ = 4.
9. If ★ represents the same whole number each time and 5 × ★ + 6 = 51, what number does ★ stand for?
9
Subtract 6 from 51 to get 45, then divide by 5: ★ = 9.
10. If ★ represents the same whole number each time and 8 × ★ + 11 = 67, what number does ★ stand for?
7
Subtract 11 from 67 to get 56, then divide by 8: ★ = 7.
11. If ★ represents the same whole number each time and 4 × ★ + 3 = 47, what number does ★ stand for?
11
Subtract 3 from 47 to get 44, then divide by 4: ★ = 11.
12. 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.

12 questions · Seed 77 · Age guidance, not curriculum certification