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 2 × ★ + 7 = 35, what number does ★ stand for?
2 · 7 · 35 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 10 = 55, what number does ★ stand for?
3 · 10 · 55 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 3 = 39, what number does ★ stand for?
4 · 3 · 39 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 15 = 25, what number does ★ stand for?
5 · 15 · 25 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 4 × ★ + 18 = 42, what number does ★ stand for?
4 · 18 · 42 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 8 = 28, what number does ★ stand for?
5 · 8 · 28 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 17 = 45, what number does ★ stand for?
4 · 17 · 45 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 4 × ★ + 16 = 76, what number does ★ stand for?
4 · 16 · 76 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 7 = 17, what number does ★ stand for?
2 · 7 · 17 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 16 = 128, what number does ★ stand for?
8 · 16 · 128 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 4 × ★ + 4 = 24, what number does ★ stand for?
4 · 4 · 24 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 6 × ★ + 3 = 75, what number does ★ stand for?
6 · 3 · 75 · Symbol equation puzzles

12 questions · Seed 104745 · 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 2 × ★ + 7 = 35, what number does ★ stand for?
14
Subtract 7 from 35 to get 28, then divide by 2: ★ = 14.
2. If ★ represents the same whole number each time and 3 × ★ + 10 = 55, what number does ★ stand for?
15
Subtract 10 from 55 to get 45, then divide by 3: ★ = 15.
3. If ★ represents the same whole number each time and 4 × ★ + 3 = 39, what number does ★ stand for?
9
Subtract 3 from 39 to get 36, then divide by 4: ★ = 9.
4. If ★ represents the same whole number each time and 5 × ★ + 15 = 25, what number does ★ stand for?
2
Subtract 15 from 25 to get 10, then divide by 5: ★ = 2.
5. If ★ represents the same whole number each time and 4 × ★ + 18 = 42, what number does ★ stand for?
6
Subtract 18 from 42 to get 24, then divide by 4: ★ = 6.
6. If ★ represents the same whole number each time and 5 × ★ + 8 = 28, what number does ★ stand for?
4
Subtract 8 from 28 to get 20, then divide by 5: ★ = 4.
7. If ★ represents the same whole number each time and 4 × ★ + 17 = 45, what number does ★ stand for?
7
Subtract 17 from 45 to get 28, then divide by 4: ★ = 7.
8. If ★ represents the same whole number each time and 4 × ★ + 16 = 76, what number does ★ stand for?
15
Subtract 16 from 76 to get 60, then divide by 4: ★ = 15.
9. If ★ represents the same whole number each time and 2 × ★ + 7 = 17, what number does ★ stand for?
5
Subtract 7 from 17 to get 10, then divide by 2: ★ = 5.
10. If ★ represents the same whole number each time and 8 × ★ + 16 = 128, what number does ★ stand for?
14
Subtract 16 from 128 to get 112, then divide by 8: ★ = 14.
11. If ★ represents the same whole number each time and 4 × ★ + 4 = 24, what number does ★ stand for?
5
Subtract 4 from 24 to get 20, then divide by 4: ★ = 5.
12. If ★ represents the same whole number each time and 6 × ★ + 3 = 75, what number does ★ stand for?
12
Subtract 3 from 75 to get 72, then divide by 6: ★ = 12.

12 questions · Seed 104745 · 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 2 × ★ + 7 = 35, what number does ★ stand for?
2 · 7 · 35 · Symbol equation puzzles
2. If ★ represents the same whole number each time and 3 × ★ + 10 = 55, what number does ★ stand for?
3 · 10 · 55 · Symbol equation puzzles
3. If ★ represents the same whole number each time and 4 × ★ + 3 = 39, what number does ★ stand for?
4 · 3 · 39 · Symbol equation puzzles
4. If ★ represents the same whole number each time and 5 × ★ + 15 = 25, what number does ★ stand for?
5 · 15 · 25 · Symbol equation puzzles
5. If ★ represents the same whole number each time and 4 × ★ + 18 = 42, what number does ★ stand for?
4 · 18 · 42 · Symbol equation puzzles
6. If ★ represents the same whole number each time and 5 × ★ + 8 = 28, what number does ★ stand for?
5 · 8 · 28 · Symbol equation puzzles
7. If ★ represents the same whole number each time and 4 × ★ + 17 = 45, what number does ★ stand for?
4 · 17 · 45 · Symbol equation puzzles
8. If ★ represents the same whole number each time and 4 × ★ + 16 = 76, what number does ★ stand for?
4 · 16 · 76 · Symbol equation puzzles
9. If ★ represents the same whole number each time and 2 × ★ + 7 = 17, what number does ★ stand for?
2 · 7 · 17 · Symbol equation puzzles
10. If ★ represents the same whole number each time and 8 × ★ + 16 = 128, what number does ★ stand for?
8 · 16 · 128 · Symbol equation puzzles
11. If ★ represents the same whole number each time and 4 × ★ + 4 = 24, what number does ★ stand for?
4 · 4 · 24 · Symbol equation puzzles
12. If ★ represents the same whole number each time and 6 × ★ + 3 = 75, what number does ★ stand for?
6 · 3 · 75 · Symbol equation puzzles

12 questions · Seed 104745 · 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 2 × ★ + 7 = 35, what number does ★ stand for?
14
Subtract 7 from 35 to get 28, then divide by 2: ★ = 14.
2. If ★ represents the same whole number each time and 3 × ★ + 10 = 55, what number does ★ stand for?
15
Subtract 10 from 55 to get 45, then divide by 3: ★ = 15.
3. If ★ represents the same whole number each time and 4 × ★ + 3 = 39, what number does ★ stand for?
9
Subtract 3 from 39 to get 36, then divide by 4: ★ = 9.
4. If ★ represents the same whole number each time and 5 × ★ + 15 = 25, what number does ★ stand for?
2
Subtract 15 from 25 to get 10, then divide by 5: ★ = 2.
5. If ★ represents the same whole number each time and 4 × ★ + 18 = 42, what number does ★ stand for?
6
Subtract 18 from 42 to get 24, then divide by 4: ★ = 6.
6. If ★ represents the same whole number each time and 5 × ★ + 8 = 28, what number does ★ stand for?
4
Subtract 8 from 28 to get 20, then divide by 5: ★ = 4.
7. If ★ represents the same whole number each time and 4 × ★ + 17 = 45, what number does ★ stand for?
7
Subtract 17 from 45 to get 28, then divide by 4: ★ = 7.
8. If ★ represents the same whole number each time and 4 × ★ + 16 = 76, what number does ★ stand for?
15
Subtract 16 from 76 to get 60, then divide by 4: ★ = 15.
9. If ★ represents the same whole number each time and 2 × ★ + 7 = 17, what number does ★ stand for?
5
Subtract 7 from 17 to get 10, then divide by 2: ★ = 5.
10. If ★ represents the same whole number each time and 8 × ★ + 16 = 128, what number does ★ stand for?
14
Subtract 16 from 128 to get 112, then divide by 8: ★ = 14.
11. If ★ represents the same whole number each time and 4 × ★ + 4 = 24, what number does ★ stand for?
5
Subtract 4 from 24 to get 20, then divide by 4: ★ = 5.
12. If ★ represents the same whole number each time and 6 × ★ + 3 = 75, what number does ★ stand for?
12
Subtract 3 from 75 to get 72, then divide by 6: ★ = 12.

12 questions · Seed 104745 · Age guidance, not curriculum certification