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Equation System (Olympiad) Advanced Worksheet: Focus on exam-oriented approach Equation System (Olympiad) ADVANCED

Level up your Equation System (Olympiad) skills! You're at Worksheet 8 of 10 (77% through this series). This exam hall simulation worksheet features 20 advanced-level problems with a focus on exam-oriented approach. Topics covered: equation system (olympiad) bank exam questions, equation system (olympiad) ssc cgl, equation system (olympiad) reasoning tricks.

📝 Worksheet 8 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Advanced level

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Worksheet 8 of 10 (77% complete)

Question 1

The sum of A and B's ages is 43. Twice A's age minus B's age is 23. Find A's age.
A + B = 43
2A - B = 23
Adding the two equations: (A + B) + (2A - B) = 43 + 23
3A = 66
A = 22
Verification: B = 43 - 22 = 21
2(22) - 21 = 23 = 23 ✓

Question 2

The sum of A and B's ages is 46. Twice A's age minus B's age is 5. Find A's age.
A + B = 46
2A - B = 5
Adding the two equations: (A + B) + (2A - B) = 46 + 5
3A = 51
A = 17
Verification: B = 46 - 17 = 29
2(17) - 29 = 5 = 5 ✓

Question 3

The sum of A and B's ages is 57. Twice A's age minus B's age is 18. Find A's age.
A + B = 57
2A - B = 18
Adding the two equations: (A + B) + (2A - B) = 57 + 18
3A = 75
A = 25
Verification: B = 57 - 25 = 32
2(25) - 32 = 18 = 18 ✓

Question 4

The sum of A and B's ages is 50. Twice A's age minus B's age is 10. Find A's age.
A + B = 50
2A - B = 10
Adding the two equations: (A + B) + (2A - B) = 50 + 10
3A = 60
A = 20
Verification: B = 50 - 20 = 30
2(20) - 30 = 10 = 10 ✓

Question 5

The sum of A and B's ages is 37. Twice A's age minus B's age is 5. Find A's age.
A + B = 37
2A - B = 5
Adding the two equations: (A + B) + (2A - B) = 37 + 5
3A = 42
A = 14
Verification: B = 37 - 14 = 23
2(14) - 23 = 5 = 5 ✓

Question 6

The sum of A and B's ages is 51. Twice A's age minus B's age is 21. Find A's age.
A + B = 51
2A - B = 21
Adding the two equations: (A + B) + (2A - B) = 51 + 21
3A = 72
A = 24
Verification: B = 51 - 24 = 27
2(24) - 27 = 21 = 21 ✓

Question 7

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 8

The sum of A and B's ages is 47. Twice A's age minus B's age is 25. Find A's age.
A + B = 47
2A - B = 25
Adding the two equations: (A + B) + (2A - B) = 47 + 25
3A = 72
A = 24
Verification: B = 47 - 24 = 23
2(24) - 23 = 25 = 25 ✓

Question 9

The sum of A and B's ages is 32. Twice A's age minus B's age is 7. Find A's age.
A + B = 32
2A - B = 7
Adding the two equations: (A + B) + (2A - B) = 32 + 7
3A = 39
A = 13
Verification: B = 32 - 13 = 19
2(13) - 19 = 7 = 7 ✓

Question 10

The sum of A and B's ages is 57. Twice A's age minus B's age is 6. Find A's age.
A + B = 57
2A - B = 6
Adding the two equations: (A + B) + (2A - B) = 57 + 6
3A = 63
A = 21
Verification: B = 57 - 21 = 36
2(21) - 36 = 6 = 6 ✓

Question 11

The sum of A and B's ages is 37. Twice A's age minus B's age is 23. Find A's age.
A + B = 37
2A - B = 23
Adding the two equations: (A + B) + (2A - B) = 37 + 23
3A = 60
A = 20
Verification: B = 37 - 20 = 17
2(20) - 17 = 23 = 23 ✓

Question 12

The sum of A and B's ages is 38. Twice A's age minus B's age is 25. Find A's age.
A + B = 38
2A - B = 25
Adding the two equations: (A + B) + (2A - B) = 38 + 25
3A = 63
A = 21
Verification: B = 38 - 21 = 17
2(21) - 17 = 25 = 25 ✓

Question 13

The sum of A and B's ages is 37. Twice A's age minus B's age is 5. Find A's age.
A + B = 37
2A - B = 5
Adding the two equations: (A + B) + (2A - B) = 37 + 5
3A = 42
A = 14
Verification: B = 37 - 14 = 23
2(14) - 23 = 5 = 5 ✓

Question 14

The sum of A and B's ages is 47. Twice A's age minus B's age is 19. Find A's age.
A + B = 47
2A - B = 19
Adding the two equations: (A + B) + (2A - B) = 47 + 19
3A = 66
A = 22
Verification: B = 47 - 22 = 25
2(22) - 25 = 19 = 19 ✓

Question 15

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 16

The sum of A and B's ages is 36. Twice A's age minus B's age is 24. Find A's age.
A + B = 36
2A - B = 24
Adding the two equations: (A + B) + (2A - B) = 36 + 24
3A = 60
A = 20
Verification: B = 36 - 20 = 16
2(20) - 16 = 24 = 24 ✓

Question 17

The sum of A and B's ages is 50. Twice A's age minus B's age is 16. Find A's age.
A + B = 50
2A - B = 16
Adding the two equations: (A + B) + (2A - B) = 50 + 16
3A = 66
A = 22
Verification: B = 50 - 22 = 28
2(22) - 28 = 16 = 16 ✓

Question 18

The sum of A and B's ages is 54. Twice A's age minus B's age is 9. Find A's age.
A + B = 54
2A - B = 9
Adding the two equations: (A + B) + (2A - B) = 54 + 9
3A = 63
A = 21
Verification: B = 54 - 21 = 33
2(21) - 33 = 9 = 9 ✓

Question 19

The sum of A and B's ages is 47. Twice A's age minus B's age is 10. Find A's age.
A + B = 47
2A - B = 10
Adding the two equations: (A + B) + (2A - B) = 47 + 10
3A = 57
A = 19
Verification: B = 47 - 19 = 28
2(19) - 28 = 10 = 10 ✓

Question 20

The sum of A and B's ages is 44. Twice A's age minus B's age is 25. Find A's age.
A + B = 44
2A - B = 25
Adding the two equations: (A + B) + (2A - B) = 44 + 25
3A = 69
A = 23
Verification: B = 44 - 23 = 21
2(23) - 21 = 25 = 25 ✓
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