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 7 × ★ + 20 = 55, what number does ★ stand for?
2. If ★ represents the same whole number each time and 2 × ★ + 6 = 14, what number does ★ stand for?
3. If ★ represents the same whole number each time and 7 × ★ + 15 = 64, what number does ★ stand for?
4. If ★ represents the same whole number each time and 2 × ★ + 3 = 21, what number does ★ stand for?
5. If ★ represents the same whole number each time and 4 × ★ + 10 = 62, what number does ★ stand for?
6. If ★ represents the same whole number each time and 8 × ★ + 2 = 66, what number does ★ stand for?
7. If ★ represents the same whole number each time and 3 × ★ + 11 = 53, what number does ★ stand for?
8. If ★ represents the same whole number each time and 4 × ★ + 12 = 64, what number does ★ stand for?
9. If ★ represents the same whole number each time and 7 × ★ + 5 = 33, what number does ★ stand for?
10. If ★ represents the same whole number each time and 8 × ★ + 11 = 59, what number does ★ stand for?
11. If ★ represents the same whole number each time and 4 × ★ + 10 = 58, what number does ★ stand for?
12. If ★ represents the same whole number each time and 7 × ★ + 9 = 30, what number does ★ stand for?
12 questions · Seed 56 · 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 = 55, what number does ★ stand for?
5Subtract 20 from 55 to get 35, then divide by 7: ★ = 5.
2. If ★ represents the same whole number each time and 2 × ★ + 6 = 14, what number does ★ stand for?
4Subtract 6 from 14 to get 8, then divide by 2: ★ = 4.
3. If ★ represents the same whole number each time and 7 × ★ + 15 = 64, what number does ★ stand for?
7Subtract 15 from 64 to get 49, then divide by 7: ★ = 7.
4. If ★ represents the same whole number each time and 2 × ★ + 3 = 21, what number does ★ stand for?
9Subtract 3 from 21 to get 18, then divide by 2: ★ = 9.
5. If ★ represents the same whole number each time and 4 × ★ + 10 = 62, what number does ★ stand for?
13Subtract 10 from 62 to get 52, then divide by 4: ★ = 13.
6. If ★ represents the same whole number each time and 8 × ★ + 2 = 66, what number does ★ stand for?
8Subtract 2 from 66 to get 64, then divide by 8: ★ = 8.
7. If ★ represents the same whole number each time and 3 × ★ + 11 = 53, what number does ★ stand for?
14Subtract 11 from 53 to get 42, then divide by 3: ★ = 14.
8. If ★ represents the same whole number each time and 4 × ★ + 12 = 64, what number does ★ stand for?
13Subtract 12 from 64 to get 52, then divide by 4: ★ = 13.
9. If ★ represents the same whole number each time and 7 × ★ + 5 = 33, what number does ★ stand for?
4Subtract 5 from 33 to get 28, then divide by 7: ★ = 4.
10. If ★ represents the same whole number each time and 8 × ★ + 11 = 59, what number does ★ stand for?
6Subtract 11 from 59 to get 48, then divide by 8: ★ = 6.
11. If ★ represents the same whole number each time and 4 × ★ + 10 = 58, what number does ★ stand for?
12Subtract 10 from 58 to get 48, then divide by 4: ★ = 12.
12. If ★ represents the same whole number each time and 7 × ★ + 9 = 30, what number does ★ stand for?
3Subtract 9 from 30 to get 21, then divide by 7: ★ = 3.
12 questions · Seed 56 · 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 = 55, what number does ★ stand for?
2. If ★ represents the same whole number each time and 2 × ★ + 6 = 14, what number does ★ stand for?
3. If ★ represents the same whole number each time and 7 × ★ + 15 = 64, what number does ★ stand for?
4. If ★ represents the same whole number each time and 2 × ★ + 3 = 21, what number does ★ stand for?
5. If ★ represents the same whole number each time and 4 × ★ + 10 = 62, what number does ★ stand for?
6. If ★ represents the same whole number each time and 8 × ★ + 2 = 66, what number does ★ stand for?
7. If ★ represents the same whole number each time and 3 × ★ + 11 = 53, what number does ★ stand for?
8. If ★ represents the same whole number each time and 4 × ★ + 12 = 64, what number does ★ stand for?
9. If ★ represents the same whole number each time and 7 × ★ + 5 = 33, what number does ★ stand for?
10. If ★ represents the same whole number each time and 8 × ★ + 11 = 59, what number does ★ stand for?
11. If ★ represents the same whole number each time and 4 × ★ + 10 = 58, what number does ★ stand for?
12. If ★ represents the same whole number each time and 7 × ★ + 9 = 30, what number does ★ stand for?
12 questions · Seed 56 · 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 = 55, what number does ★ stand for?
5Subtract 20 from 55 to get 35, then divide by 7: ★ = 5.
2. If ★ represents the same whole number each time and 2 × ★ + 6 = 14, what number does ★ stand for?
4Subtract 6 from 14 to get 8, then divide by 2: ★ = 4.
3. If ★ represents the same whole number each time and 7 × ★ + 15 = 64, what number does ★ stand for?
7Subtract 15 from 64 to get 49, then divide by 7: ★ = 7.
4. If ★ represents the same whole number each time and 2 × ★ + 3 = 21, what number does ★ stand for?
9Subtract 3 from 21 to get 18, then divide by 2: ★ = 9.
5. If ★ represents the same whole number each time and 4 × ★ + 10 = 62, what number does ★ stand for?
13Subtract 10 from 62 to get 52, then divide by 4: ★ = 13.
6. If ★ represents the same whole number each time and 8 × ★ + 2 = 66, what number does ★ stand for?
8Subtract 2 from 66 to get 64, then divide by 8: ★ = 8.
7. If ★ represents the same whole number each time and 3 × ★ + 11 = 53, what number does ★ stand for?
14Subtract 11 from 53 to get 42, then divide by 3: ★ = 14.
8. If ★ represents the same whole number each time and 4 × ★ + 12 = 64, what number does ★ stand for?
13Subtract 12 from 64 to get 52, then divide by 4: ★ = 13.
9. If ★ represents the same whole number each time and 7 × ★ + 5 = 33, what number does ★ stand for?
4Subtract 5 from 33 to get 28, then divide by 7: ★ = 4.
10. If ★ represents the same whole number each time and 8 × ★ + 11 = 59, what number does ★ stand for?
6Subtract 11 from 59 to get 48, then divide by 8: ★ = 6.
11. If ★ represents the same whole number each time and 4 × ★ + 10 = 58, what number does ★ stand for?
12Subtract 10 from 58 to get 48, then divide by 4: ★ = 12.
12. If ★ represents the same whole number each time and 7 × ★ + 9 = 30, what number does ★ stand for?
3Subtract 9 from 30 to get 21, then divide by 7: ★ = 3.
12 questions · Seed 56 · Age guidance, not curriculum certification