ReasoningAbility.com

Equation System (Olympiad): Worksheet 10 - Expert Practice Equation System (Olympiad) EXPERT

Ready to master Equation System (Olympiad)? This accuracy focus 👑 worksheet (10/10) presents 20 expert-level challenges. Focus area: application-based learning. Learn to solve equation system (olympiad) reasoning tricks, handle fast equation system (olympiad) solving, and perfect equation system (olympiad) mastery with our step-by-step solutions.

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

What you'll learn in this worksheet:
Your progress through Equation System (Olympiad)
Worksheet 10 of 10 (100% complete)

Question 1

The sum of A and B's ages is 55. Twice A's age minus B's age is 17. Find A's age.
A + B = 55
2A - B = 17
Adding the two equations: (A + B) + (2A - B) = 55 + 17
3A = 72
A = 24
Verification: B = 55 - 24 = 31
2(24) - 31 = 17 = 17 ✓

Question 2

The sum of A and B's ages is 50. Twice A's age minus B's age is 19. Find A's age.
A + B = 50
2A - B = 19
Adding the two equations: (A + B) + (2A - B) = 50 + 19
3A = 69
A = 23
Verification: B = 50 - 23 = 27
2(23) - 27 = 19 = 19 ✓

Question 3

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 4

The sum of A and B's ages is 52. Twice A's age minus B's age is 11. Find A's age.
A + B = 52
2A - B = 11
Adding the two equations: (A + B) + (2A - B) = 52 + 11
3A = 63
A = 21
Verification: B = 52 - 21 = 31
2(21) - 31 = 11 = 11 ✓

Question 5

The sum of A and B's ages is 60. Twice A's age minus B's age is 6. Find A's age.
A + B = 60
2A - B = 6
Adding the two equations: (A + B) + (2A - B) = 60 + 6
3A = 66
A = 22
Verification: B = 60 - 22 = 38
2(22) - 38 = 6 = 6 ✓

Question 6

The sum of A and B's ages is 44. Twice A's age minus B's age is 16. Find A's age.
A + B = 44
2A - B = 16
Adding the two equations: (A + B) + (2A - B) = 44 + 16
3A = 60
A = 20
Verification: B = 44 - 20 = 24
2(20) - 24 = 16 = 16 ✓

Question 7

The sum of A and B's ages is 43. Twice A's age minus B's age is 5. Find A's age.
A + B = 43
2A - B = 5
Adding the two equations: (A + B) + (2A - B) = 43 + 5
3A = 48
A = 16
Verification: B = 43 - 16 = 27
2(16) - 27 = 5 = 5 ✓

Question 8

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 9

The sum of A and B's ages is 58. Twice A's age minus B's age is 8. Find A's age.
A + B = 58
2A - B = 8
Adding the two equations: (A + B) + (2A - B) = 58 + 8
3A = 66
A = 22
Verification: B = 58 - 22 = 36
2(22) - 36 = 8 = 8 ✓

Question 10

The sum of A and B's ages is 48. Twice A's age minus B's age is 21. Find A's age.
A + B = 48
2A - B = 21
Adding the two equations: (A + B) + (2A - B) = 48 + 21
3A = 69
A = 23
Verification: B = 48 - 23 = 25
2(23) - 25 = 21 = 21 ✓

Question 11

The sum of A and B's ages is 51. Twice A's age minus B's age is 9. Find A's age.
A + B = 51
2A - B = 9
Adding the two equations: (A + B) + (2A - B) = 51 + 9
3A = 60
A = 20
Verification: B = 51 - 20 = 31
2(20) - 31 = 9 = 9 ✓

Question 12

The sum of A and B's ages is 59. Twice A's age minus B's age is 7. Find A's age.
A + B = 59
2A - B = 7
Adding the two equations: (A + B) + (2A - B) = 59 + 7
3A = 66
A = 22
Verification: B = 59 - 22 = 37
2(22) - 37 = 7 = 7 ✓

Question 13

The sum of A and B's ages is 53. Twice A's age minus B's age is 22. Find A's age.
A + B = 53
2A - B = 22
Adding the two equations: (A + B) + (2A - B) = 53 + 22
3A = 75
A = 25
Verification: B = 53 - 25 = 28
2(25) - 28 = 22 = 22 ✓

Question 14

The sum of A and B's ages is 34. Twice A's age minus B's age is 20. Find A's age.
A + B = 34
2A - B = 20
Adding the two equations: (A + B) + (2A - B) = 34 + 20
3A = 54
A = 18
Verification: B = 34 - 18 = 16
2(18) - 16 = 20 = 20 ✓

Question 15

The sum of A and B's ages is 41. Twice A's age minus B's age is 10. Find A's age.
A + B = 41
2A - B = 10
Adding the two equations: (A + B) + (2A - B) = 41 + 10
3A = 51
A = 17
Verification: B = 41 - 17 = 24
2(17) - 24 = 10 = 10 ✓

Question 16

The sum of A and B's ages is 33. Twice A's age minus B's age is 24. Find A's age.
A + B = 33
2A - B = 24
Adding the two equations: (A + B) + (2A - B) = 33 + 24
3A = 57
A = 19
Verification: B = 33 - 19 = 14
2(19) - 14 = 24 = 24 ✓

Question 17

The sum of A and B's ages is 45. Twice A's age minus B's age is 24. Find A's age.
A + B = 45
2A - B = 24
Adding the two equations: (A + B) + (2A - B) = 45 + 24
3A = 69
A = 23
Verification: B = 45 - 23 = 22
2(23) - 22 = 24 = 24 ✓

Question 18

The sum of A and B's ages is 33. Twice A's age minus B's age is 24. Find A's age.
A + B = 33
2A - B = 24
Adding the two equations: (A + B) + (2A - B) = 33 + 24
3A = 57
A = 19
Verification: B = 33 - 19 = 14
2(19) - 14 = 24 = 24 ✓

Question 19

The sum of A and B's ages is 36. Twice A's age minus B's age is 12. Find A's age.
A + B = 36
2A - B = 12
Adding the two equations: (A + B) + (2A - B) = 36 + 12
3A = 48
A = 16
Verification: B = 36 - 16 = 20
2(16) - 20 = 12 = 12 ✓

Question 20

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 ✓
Previous Worksheet