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Equation System (Olympiad): Worksheet 2 - Beginner Practice Equation System (Olympiad) BEGINNER

Ready to master Equation System (Olympiad)? This entry level practice worksheet (2/10) presents 20 beginner-level challenges. Focus area: pattern recognition. Learn to solve equation system (olympiad) reasoning questions, handle equation system (olympiad) practice, and perfect equation system (olympiad) for competitive exams with our step-by-step solutions.

📝 Worksheet 2 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner level

What you'll learn in this worksheet:
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Worksheet 2 of 10 (11% complete)

Question 1

The sum of A and B's ages is 45. Twice A's age minus B's age is 6. Find A's age.
A + B = 45
2A - B = 6
Adding the two equations: (A + B) + (2A - B) = 45 + 6
3A = 51
A = 17
Verification: B = 45 - 17 = 28
2(17) - 28 = 6 = 6 ✓

Question 2

The sum of A and B's ages is 35. Twice A's age minus B's age is 25. Find A's age.
A + B = 35
2A - B = 25
Adding the two equations: (A + B) + (2A - B) = 35 + 25
3A = 60
A = 20
Verification: B = 35 - 20 = 15
2(20) - 15 = 25 = 25 ✓

Question 3

The sum of A and B's ages is 39. Twice A's age minus B's age is 15. Find A's age.
A + B = 39
2A - B = 15
Adding the two equations: (A + B) + (2A - B) = 39 + 15
3A = 54
A = 18
Verification: B = 39 - 18 = 21
2(18) - 21 = 15 = 15 ✓

Question 4

The sum of A and B's ages is 45. Twice A's age minus B's age is 9. Find A's age.
A + B = 45
2A - B = 9
Adding the two equations: (A + B) + (2A - B) = 45 + 9
3A = 54
A = 18
Verification: B = 45 - 18 = 27
2(18) - 27 = 9 = 9 ✓

Question 5

The sum of A and B's ages is 58. Twice A's age minus B's age is 20. Find A's age.
A + B = 58
2A - B = 20
Adding the two equations: (A + B) + (2A - B) = 58 + 20
3A = 78
A = 26
Verification: B = 58 - 26 = 32
2(26) - 32 = 20 = 20 ✓

Question 6

The sum of A and B's ages is 60. Twice A's age minus B's age is 12. Find A's age.
A + B = 60
2A - B = 12
Adding the two equations: (A + B) + (2A - B) = 60 + 12
3A = 72
A = 24
Verification: B = 60 - 24 = 36
2(24) - 36 = 12 = 12 ✓

Question 7

The sum of A and B's ages is 32. Twice A's age minus B's age is 19. Find A's age.
A + B = 32
2A - B = 19
Adding the two equations: (A + B) + (2A - B) = 32 + 19
3A = 51
A = 17
Verification: B = 32 - 17 = 15
2(17) - 15 = 19 = 19 ✓

Question 8

The sum of A and B's ages is 51. Twice A's age minus B's age is 18. Find A's age.
A + B = 51
2A - B = 18
Adding the two equations: (A + B) + (2A - B) = 51 + 18
3A = 69
A = 23
Verification: B = 51 - 23 = 28
2(23) - 28 = 18 = 18 ✓

Question 9

The sum of A and B's ages is 54. Twice A's age minus B's age is 6. Find A's age.
A + B = 54
2A - B = 6
Adding the two equations: (A + B) + (2A - B) = 54 + 6
3A = 60
A = 20
Verification: B = 54 - 20 = 34
2(20) - 34 = 6 = 6 ✓

Question 10

The sum of A and B's ages is 39. Twice A's age minus B's age is 6. Find A's age.
A + B = 39
2A - B = 6
Adding the two equations: (A + B) + (2A - B) = 39 + 6
3A = 45
A = 15
Verification: B = 39 - 15 = 24
2(15) - 24 = 6 = 6 ✓

Question 11

The sum of A and B's ages is 59. Twice A's age minus B's age is 10. Find A's age.
A + B = 59
2A - B = 10
Adding the two equations: (A + B) + (2A - B) = 59 + 10
3A = 69
A = 23
Verification: B = 59 - 23 = 36
2(23) - 36 = 10 = 10 ✓

Question 12

The sum of A and B's ages is 30. Twice A's age minus B's age is 6. Find A's age.
A + B = 30
2A - B = 6
Adding the two equations: (A + B) + (2A - B) = 30 + 6
3A = 36
A = 12
Verification: B = 30 - 12 = 18
2(12) - 18 = 6 = 6 ✓

Question 13

The sum of A and B's ages is 59. Twice A's age minus B's age is 25. Find A's age.
A + B = 59
2A - B = 25
Adding the two equations: (A + B) + (2A - B) = 59 + 25
3A = 84
A = 28
Verification: B = 59 - 28 = 31
2(28) - 31 = 25 = 25 ✓

Question 14

The sum of A and B's ages is 33. Twice A's age minus B's age is 12. Find A's age.
A + B = 33
2A - B = 12
Adding the two equations: (A + B) + (2A - B) = 33 + 12
3A = 45
A = 15
Verification: B = 33 - 15 = 18
2(15) - 18 = 12 = 12 ✓

Question 15

The sum of A and B's ages is 55. Twice A's age minus B's age is 11. Find A's age.
A + B = 55
2A - B = 11
Adding the two equations: (A + B) + (2A - B) = 55 + 11
3A = 66
A = 22
Verification: B = 55 - 22 = 33
2(22) - 33 = 11 = 11 ✓

Question 16

The sum of A and B's ages is 35. Twice A's age minus B's age is 22. Find A's age.
A + B = 35
2A - B = 22
Adding the two equations: (A + B) + (2A - B) = 35 + 22
3A = 57
A = 19
Verification: B = 35 - 19 = 16
2(19) - 16 = 22 = 22 ✓

Question 17

The sum of A and B's ages is 39. Twice A's age minus B's age is 6. Find A's age.
A + B = 39
2A - B = 6
Adding the two equations: (A + B) + (2A - B) = 39 + 6
3A = 45
A = 15
Verification: B = 39 - 15 = 24
2(15) - 24 = 6 = 6 ✓

Question 18

The sum of A and B's ages is 45. Twice A's age minus B's age is 6. Find A's age.
A + B = 45
2A - B = 6
Adding the two equations: (A + B) + (2A - B) = 45 + 6
3A = 51
A = 17
Verification: B = 45 - 17 = 28
2(17) - 28 = 6 = 6 ✓

Question 19

The sum of A and B's ages is 34. Twice A's age minus B's age is 8. Find A's age.
A + B = 34
2A - B = 8
Adding the two equations: (A + B) + (2A - B) = 34 + 8
3A = 42
A = 14
Verification: B = 34 - 14 = 20
2(14) - 20 = 8 = 8 ✓

Question 20

The sum of A and B's ages is 38. Twice A's age minus B's age is 16. Find A's age.
A + B = 38
2A - B = 16
Adding the two equations: (A + B) + (2A - B) = 38 + 16
3A = 54
A = 18
Verification: B = 38 - 18 = 20
2(18) - 20 = 16 = 16 ✓
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