Back to worksheetsReasoningAges 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.
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 × ★ + 17 = 32, what number does ★ stand for?
2. If ★ represents the same whole number each time and 7 × ★ + 7 = 28, what number does ★ stand for?
3. If ★ represents the same whole number each time and 2 × ★ + 4 = 10, what number does ★ stand for?
4. If ★ represents the same whole number each time and 4 × ★ + 13 = 25, what number does ★ stand for?
5. If ★ represents the same whole number each time and 7 × ★ + 12 = 40, what number does ★ stand for?
6. If ★ represents the same whole number each time and 8 × ★ + 2 = 42, what number does ★ stand for?
7. If ★ represents the same whole number each time and 4 × ★ + 18 = 70, what number does ★ stand for?
8. If ★ represents the same whole number each time and 4 × ★ + 20 = 48, what number does ★ stand for?
9. If ★ represents the same whole number each time and 5 × ★ + 2 = 17, what number does ★ stand for?
10. If ★ represents the same whole number each time and 3 × ★ + 12 = 24, what number does ★ stand for?
11. If ★ represents the same whole number each time and 3 × ★ + 14 = 20, what number does ★ stand for?
12. If ★ represents the same whole number each time and 7 × ★ + 19 = 68, what number does ★ stand for?
12 questions · Seed 51 · 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 × ★ + 17 = 32, what number does ★ stand for?
3Subtract 17 from 32 to get 15, then divide by 5: ★ = 3.
2. If ★ represents the same whole number each time and 7 × ★ + 7 = 28, what number does ★ stand for?
3Subtract 7 from 28 to get 21, then divide by 7: ★ = 3.
3. If ★ represents the same whole number each time and 2 × ★ + 4 = 10, what number does ★ stand for?
3Subtract 4 from 10 to get 6, then divide by 2: ★ = 3.
4. If ★ represents the same whole number each time and 4 × ★ + 13 = 25, what number does ★ stand for?
3Subtract 13 from 25 to get 12, then divide by 4: ★ = 3.
5. If ★ represents the same whole number each time and 7 × ★ + 12 = 40, what number does ★ stand for?
4Subtract 12 from 40 to get 28, then divide by 7: ★ = 4.
6. If ★ represents the same whole number each time and 8 × ★ + 2 = 42, what number does ★ stand for?
5Subtract 2 from 42 to get 40, then divide by 8: ★ = 5.
7. If ★ represents the same whole number each time and 4 × ★ + 18 = 70, what number does ★ stand for?
13Subtract 18 from 70 to get 52, then divide by 4: ★ = 13.
8. If ★ represents the same whole number each time and 4 × ★ + 20 = 48, what number does ★ stand for?
7Subtract 20 from 48 to get 28, then divide by 4: ★ = 7.
9. If ★ represents the same whole number each time and 5 × ★ + 2 = 17, what number does ★ stand for?
3Subtract 2 from 17 to get 15, then divide by 5: ★ = 3.
10. If ★ represents the same whole number each time and 3 × ★ + 12 = 24, what number does ★ stand for?
4Subtract 12 from 24 to get 12, then divide by 3: ★ = 4.
11. If ★ represents the same whole number each time and 3 × ★ + 14 = 20, what number does ★ stand for?
2Subtract 14 from 20 to get 6, then divide by 3: ★ = 2.
12. If ★ represents the same whole number each time and 7 × ★ + 19 = 68, what number does ★ stand for?
7Subtract 19 from 68 to get 49, then divide by 7: ★ = 7.
12 questions · Seed 51 · 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 × ★ + 17 = 32, what number does ★ stand for?
2. If ★ represents the same whole number each time and 7 × ★ + 7 = 28, what number does ★ stand for?
3. If ★ represents the same whole number each time and 2 × ★ + 4 = 10, what number does ★ stand for?
4. If ★ represents the same whole number each time and 4 × ★ + 13 = 25, what number does ★ stand for?
5. If ★ represents the same whole number each time and 7 × ★ + 12 = 40, what number does ★ stand for?
6. If ★ represents the same whole number each time and 8 × ★ + 2 = 42, what number does ★ stand for?
7. If ★ represents the same whole number each time and 4 × ★ + 18 = 70, what number does ★ stand for?
8. If ★ represents the same whole number each time and 4 × ★ + 20 = 48, what number does ★ stand for?
9. If ★ represents the same whole number each time and 5 × ★ + 2 = 17, what number does ★ stand for?
10. If ★ represents the same whole number each time and 3 × ★ + 12 = 24, what number does ★ stand for?
11. If ★ represents the same whole number each time and 3 × ★ + 14 = 20, what number does ★ stand for?
12. If ★ represents the same whole number each time and 7 × ★ + 19 = 68, what number does ★ stand for?
12 questions · Seed 51 · 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 × ★ + 17 = 32, what number does ★ stand for?
3Subtract 17 from 32 to get 15, then divide by 5: ★ = 3.
2. If ★ represents the same whole number each time and 7 × ★ + 7 = 28, what number does ★ stand for?
3Subtract 7 from 28 to get 21, then divide by 7: ★ = 3.
3. If ★ represents the same whole number each time and 2 × ★ + 4 = 10, what number does ★ stand for?
3Subtract 4 from 10 to get 6, then divide by 2: ★ = 3.
4. If ★ represents the same whole number each time and 4 × ★ + 13 = 25, what number does ★ stand for?
3Subtract 13 from 25 to get 12, then divide by 4: ★ = 3.
5. If ★ represents the same whole number each time and 7 × ★ + 12 = 40, what number does ★ stand for?
4Subtract 12 from 40 to get 28, then divide by 7: ★ = 4.
6. If ★ represents the same whole number each time and 8 × ★ + 2 = 42, what number does ★ stand for?
5Subtract 2 from 42 to get 40, then divide by 8: ★ = 5.
7. If ★ represents the same whole number each time and 4 × ★ + 18 = 70, what number does ★ stand for?
13Subtract 18 from 70 to get 52, then divide by 4: ★ = 13.
8. If ★ represents the same whole number each time and 4 × ★ + 20 = 48, what number does ★ stand for?
7Subtract 20 from 48 to get 28, then divide by 4: ★ = 7.
9. If ★ represents the same whole number each time and 5 × ★ + 2 = 17, what number does ★ stand for?
3Subtract 2 from 17 to get 15, then divide by 5: ★ = 3.
10. If ★ represents the same whole number each time and 3 × ★ + 12 = 24, what number does ★ stand for?
4Subtract 12 from 24 to get 12, then divide by 3: ★ = 4.
11. If ★ represents the same whole number each time and 3 × ★ + 14 = 20, what number does ★ stand for?
2Subtract 14 from 20 to get 6, then divide by 3: ★ = 2.
12. If ★ represents the same whole number each time and 7 × ★ + 19 = 68, what number does ★ stand for?
7Subtract 19 from 68 to get 49, then divide by 7: ★ = 7.
12 questions · Seed 51 · Age guidance, not curriculum certification