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 × ★ + 4 = 95, what number does ★ stand for?
7 · 4 · 95 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 15 = 99, what number does ★ stand for?
6 · 15 · 99 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 9 = 57, what number does ★ stand for?
4 · 9 · 57 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 8 = 68, what number does ★ stand for?
6 · 8 · 68 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 15 = 51, what number does ★ stand for?
3 · 15 · 51 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 3 = 31, what number does ★ stand for?
2 · 3 · 31 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 14 = 54, what number does ★ stand for?
5 · 14 · 54 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 2 × ★ + 17 = 35, what number does ★ stand for?
2 · 17 · 35 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 3 × ★ + 3 = 15, what number does ★ stand for?
3 · 3 · 15 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 6 × ★ + 3 = 87, what number does ★ stand for?
6 · 3 · 87 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 17 = 56, what number does ★ stand for?
3 · 17 · 56 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 20 = 34, what number does ★ stand for?
7 · 20 · 34 · Symbol equation puzzles

12 questions · Seed 72 · 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 × ★ + 4 = 95, what number does ★ stand for?
13
Subtract 4 from 95 to get 91, then divide by 7: ★ = 13.
2. If ★ represents the same whole number each time and 6 × ★ + 15 = 99, what number does ★ stand for?
14
Subtract 15 from 99 to get 84, then divide by 6: ★ = 14.
3. If ★ represents the same whole number each time and 4 × ★ + 9 = 57, what number does ★ stand for?
12
Subtract 9 from 57 to get 48, then divide by 4: ★ = 12.
4. If ★ represents the same whole number each time and 6 × ★ + 8 = 68, what number does ★ stand for?
10
Subtract 8 from 68 to get 60, then divide by 6: ★ = 10.
5. If ★ represents the same whole number each time and 3 × ★ + 15 = 51, what number does ★ stand for?
12
Subtract 15 from 51 to get 36, then divide by 3: ★ = 12.
6. If ★ represents the same whole number each time and 2 × ★ + 3 = 31, what number does ★ stand for?
14
Subtract 3 from 31 to get 28, then divide by 2: ★ = 14.
7. If ★ represents the same whole number each time and 5 × ★ + 14 = 54, what number does ★ stand for?
8
Subtract 14 from 54 to get 40, then divide by 5: ★ = 8.
8. If ★ represents the same whole number each time and 2 × ★ + 17 = 35, what number does ★ stand for?
9
Subtract 17 from 35 to get 18, then divide by 2: ★ = 9.
9. If ★ represents the same whole number each time and 3 × ★ + 3 = 15, what number does ★ stand for?
4
Subtract 3 from 15 to get 12, then divide by 3: ★ = 4.
10. If ★ represents the same whole number each time and 6 × ★ + 3 = 87, what number does ★ stand for?
14
Subtract 3 from 87 to get 84, then divide by 6: ★ = 14.
11. If ★ represents the same whole number each time and 3 × ★ + 17 = 56, what number does ★ stand for?
13
Subtract 17 from 56 to get 39, then divide by 3: ★ = 13.
12. If ★ represents the same whole number each time and 7 × ★ + 20 = 34, what number does ★ stand for?
2
Subtract 20 from 34 to get 14, then divide by 7: ★ = 2.

12 questions · Seed 72 · 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 × ★ + 4 = 95, what number does ★ stand for?
7 · 4 · 95 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 6 × ★ + 15 = 99, what number does ★ stand for?
6 · 15 · 99 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 9 = 57, what number does ★ stand for?
4 · 9 · 57 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 6 × ★ + 8 = 68, what number does ★ stand for?
6 · 8 · 68 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 3 × ★ + 15 = 51, what number does ★ stand for?
3 · 15 · 51 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 2 × ★ + 3 = 31, what number does ★ stand for?
2 · 3 · 31 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 5 × ★ + 14 = 54, what number does ★ stand for?
5 · 14 · 54 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 2 × ★ + 17 = 35, what number does ★ stand for?
2 · 17 · 35 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 3 × ★ + 3 = 15, what number does ★ stand for?
3 · 3 · 15 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 6 × ★ + 3 = 87, what number does ★ stand for?
6 · 3 · 87 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 3 × ★ + 17 = 56, what number does ★ stand for?
3 · 17 · 56 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 7 × ★ + 20 = 34, what number does ★ stand for?
7 · 20 · 34 · Symbol equation puzzles

12 questions · Seed 72 · 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 × ★ + 4 = 95, what number does ★ stand for?
13
Subtract 4 from 95 to get 91, then divide by 7: ★ = 13.
2. If ★ represents the same whole number each time and 6 × ★ + 15 = 99, what number does ★ stand for?
14
Subtract 15 from 99 to get 84, then divide by 6: ★ = 14.
3. If ★ represents the same whole number each time and 4 × ★ + 9 = 57, what number does ★ stand for?
12
Subtract 9 from 57 to get 48, then divide by 4: ★ = 12.
4. If ★ represents the same whole number each time and 6 × ★ + 8 = 68, what number does ★ stand for?
10
Subtract 8 from 68 to get 60, then divide by 6: ★ = 10.
5. If ★ represents the same whole number each time and 3 × ★ + 15 = 51, what number does ★ stand for?
12
Subtract 15 from 51 to get 36, then divide by 3: ★ = 12.
6. If ★ represents the same whole number each time and 2 × ★ + 3 = 31, what number does ★ stand for?
14
Subtract 3 from 31 to get 28, then divide by 2: ★ = 14.
7. If ★ represents the same whole number each time and 5 × ★ + 14 = 54, what number does ★ stand for?
8
Subtract 14 from 54 to get 40, then divide by 5: ★ = 8.
8. If ★ represents the same whole number each time and 2 × ★ + 17 = 35, what number does ★ stand for?
9
Subtract 17 from 35 to get 18, then divide by 2: ★ = 9.
9. If ★ represents the same whole number each time and 3 × ★ + 3 = 15, what number does ★ stand for?
4
Subtract 3 from 15 to get 12, then divide by 3: ★ = 4.
10. If ★ represents the same whole number each time and 6 × ★ + 3 = 87, what number does ★ stand for?
14
Subtract 3 from 87 to get 84, then divide by 6: ★ = 14.
11. If ★ represents the same whole number each time and 3 × ★ + 17 = 56, what number does ★ stand for?
13
Subtract 17 from 56 to get 39, then divide by 3: ★ = 13.
12. If ★ represents the same whole number each time and 7 × ★ + 20 = 34, what number does ★ stand for?
2
Subtract 20 from 34 to get 14, then divide by 7: ★ = 2.

12 questions · Seed 72 · Age guidance, not curriculum certification