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Equation System (Olympiad) - Expert Level: conceptual clarity Equation System (Olympiad) EXPERT

This skill evaluation ⚡ worksheet focuses on Equation System (Olympiad) - a key topic in Age Problems. You'll solve 20 expert-level problems (Worksheet 9 of 10). The primary focus is on conceptual clarity. Master equation system (olympiad) ssc cgl, equation system (olympiad) reasoning tricks, and fast equation system (olympiad) solving through systematic practice.

📝 Worksheet 9 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Expert level

What you'll learn in this worksheet:
Your progress through Equation System (Olympiad)
Worksheet 9 of 10 (88% complete)

Question 1

The sum of A and B's ages is 50. Twice A's age minus B's age is 13. Find A's age.
A + B = 50
2A - B = 13
Adding the two equations: (A + B) + (2A - B) = 50 + 13
3A = 63
A = 21
Verification: B = 50 - 21 = 29
2(21) - 29 = 13 = 13 ✓

Question 2

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 3

The sum of A and B's ages is 42. Twice A's age minus B's age is 15. Find A's age.
A + B = 42
2A - B = 15
Adding the two equations: (A + B) + (2A - B) = 42 + 15
3A = 57
A = 19
Verification: B = 42 - 19 = 23
2(19) - 23 = 15 = 15 ✓

Question 4

The sum of A and B's ages is 57. Twice A's age minus B's age is 9. Find A's age.
A + B = 57
2A - B = 9
Adding the two equations: (A + B) + (2A - B) = 57 + 9
3A = 66
A = 22
Verification: B = 57 - 22 = 35
2(22) - 35 = 9 = 9 ✓

Question 5

The sum of A and B's ages is 40. Twice A's age minus B's age is 8. Find A's age.
A + B = 40
2A - B = 8
Adding the two equations: (A + B) + (2A - B) = 40 + 8
3A = 48
A = 16
Verification: B = 40 - 16 = 24
2(16) - 24 = 8 = 8 ✓

Question 6

The sum of A and B's ages is 36. Twice A's age minus B's age is 21. Find A's age.
A + B = 36
2A - B = 21
Adding the two equations: (A + B) + (2A - B) = 36 + 21
3A = 57
A = 19
Verification: B = 36 - 19 = 17
2(19) - 17 = 21 = 21 ✓

Question 7

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 8

The sum of A and B's ages is 35. Twice A's age minus B's age is 10. Find A's age.
A + B = 35
2A - B = 10
Adding the two equations: (A + B) + (2A - B) = 35 + 10
3A = 45
A = 15
Verification: B = 35 - 15 = 20
2(15) - 20 = 10 = 10 ✓

Question 9

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 10

The sum of A and B's ages is 39. Twice A's age minus B's age is 9. Find A's age.
A + B = 39
2A - B = 9
Adding the two equations: (A + B) + (2A - B) = 39 + 9
3A = 48
A = 16
Verification: B = 39 - 16 = 23
2(16) - 23 = 9 = 9 ✓

Question 11

The sum of A and B's ages is 55. Twice A's age minus B's age is 14. Find A's age.
A + B = 55
2A - B = 14
Adding the two equations: (A + B) + (2A - B) = 55 + 14
3A = 69
A = 23
Verification: B = 55 - 23 = 32
2(23) - 32 = 14 = 14 ✓

Question 12

The sum of A and B's ages is 51. Twice A's age minus B's age is 24. Find A's age.
A + B = 51
2A - B = 24
Adding the two equations: (A + B) + (2A - B) = 51 + 24
3A = 75
A = 25
Verification: B = 51 - 25 = 26
2(25) - 26 = 24 = 24 ✓

Question 13

The sum of A and B's ages is 37. Twice A's age minus B's age is 20. Find A's age.
A + B = 37
2A - B = 20
Adding the two equations: (A + B) + (2A - B) = 37 + 20
3A = 57
A = 19
Verification: B = 37 - 19 = 18
2(19) - 18 = 20 = 20 ✓

Question 14

The sum of A and B's ages is 37. Twice A's age minus B's age is 8. Find A's age.
A + B = 37
2A - B = 8
Adding the two equations: (A + B) + (2A - B) = 37 + 8
3A = 45
A = 15
Verification: B = 37 - 15 = 22
2(15) - 22 = 8 = 8 ✓

Question 15

The sum of A and B's ages is 45. Twice A's age minus B's age is 18. Find A's age.
A + B = 45
2A - B = 18
Adding the two equations: (A + B) + (2A - B) = 45 + 18
3A = 63
A = 21
Verification: B = 45 - 21 = 24
2(21) - 24 = 18 = 18 ✓

Question 16

The sum of A and B's ages is 55. Twice A's age minus B's age is 5. Find A's age.
A + B = 55
2A - B = 5
Adding the two equations: (A + B) + (2A - B) = 55 + 5
3A = 60
A = 20
Verification: B = 55 - 20 = 35
2(20) - 35 = 5 = 5 ✓

Question 17

The sum of A and B's ages is 49. Twice A's age minus B's age is 8. Find A's age.
A + B = 49
2A - B = 8
Adding the two equations: (A + B) + (2A - B) = 49 + 8
3A = 57
A = 19
Verification: B = 49 - 19 = 30
2(19) - 30 = 8 = 8 ✓

Question 18

The sum of A and B's ages is 52. Twice A's age minus B's age is 8. Find A's age.
A + B = 52
2A - B = 8
Adding the two equations: (A + B) + (2A - B) = 52 + 8
3A = 60
A = 20
Verification: B = 52 - 20 = 32
2(20) - 32 = 8 = 8 ✓

Question 19

The sum of A and B's ages is 49. Twice A's age minus B's age is 20. Find A's age.
A + B = 49
2A - B = 20
Adding the two equations: (A + B) + (2A - B) = 49 + 20
3A = 69
A = 23
Verification: B = 49 - 23 = 26
2(23) - 26 = 20 = 20 ✓

Question 20

The sum of A and B's ages is 53. Twice A's age minus B's age is 10. Find A's age.
A + B = 53
2A - B = 10
Adding the two equations: (A + B) + (2A - B) = 53 + 10
3A = 63
A = 21
Verification: B = 53 - 21 = 32
2(21) - 32 = 10 = 10 ✓
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