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Equation System (Olympiad) - Intermediate Level: tricky scenarios handling Equation System (Olympiad) INTERMEDIATE

This expert challenge 📈 worksheet focuses on Equation System (Olympiad) - a key topic in Age Problems. You'll solve 20 intermediate-level problems (Worksheet 5 of 10). The primary focus is on tricky scenarios handling. Master how to solve equation system (olympiad), equation system (olympiad) tricks, and equation system (olympiad) shortcut methods through systematic practice.

📝 Worksheet 5 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Equation System (Olympiad)
Worksheet 5 of 10 (44% complete)

Question 1

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 2

The sum of A and B's ages is 48. Twice A's age minus B's age is 6. Find A's age.
A + B = 48
2A - B = 6
Adding the two equations: (A + B) + (2A - B) = 48 + 6
3A = 54
A = 18
Verification: B = 48 - 18 = 30
2(18) - 30 = 6 = 6 ✓

Question 3

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 4

The sum of A and B's ages is 44. Twice A's age minus B's age is 19. Find A's age.
A + B = 44
2A - B = 19
Adding the two equations: (A + B) + (2A - B) = 44 + 19
3A = 63
A = 21
Verification: B = 44 - 21 = 23
2(21) - 23 = 19 = 19 ✓

Question 5

The sum of A and B's ages is 57. Twice A's age minus B's age is 21. Find A's age.
A + B = 57
2A - B = 21
Adding the two equations: (A + B) + (2A - B) = 57 + 21
3A = 78
A = 26
Verification: B = 57 - 26 = 31
2(26) - 31 = 21 = 21 ✓

Question 6

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 7

The sum of A and B's ages is 58. Twice A's age minus B's age is 11. Find A's age.
A + B = 58
2A - B = 11
Adding the two equations: (A + B) + (2A - B) = 58 + 11
3A = 69
A = 23
Verification: B = 58 - 23 = 35
2(23) - 35 = 11 = 11 ✓

Question 8

The sum of A and B's ages is 45. Twice A's age minus B's age is 15. Find A's age.
A + B = 45
2A - B = 15
Adding the two equations: (A + B) + (2A - B) = 45 + 15
3A = 60
A = 20
Verification: B = 45 - 20 = 25
2(20) - 25 = 15 = 15 ✓

Question 9

The sum of A and B's ages is 43. Twice A's age minus B's age is 20. Find A's age.
A + B = 43
2A - B = 20
Adding the two equations: (A + B) + (2A - B) = 43 + 20
3A = 63
A = 21
Verification: B = 43 - 21 = 22
2(21) - 22 = 20 = 20 ✓

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 40. Twice A's age minus B's age is 17. Find A's age.
A + B = 40
2A - B = 17
Adding the two equations: (A + B) + (2A - B) = 40 + 17
3A = 57
A = 19
Verification: B = 40 - 19 = 21
2(19) - 21 = 17 = 17 ✓

Question 12

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 13

The sum of A and B's ages is 34. Twice A's age minus B's age is 11. Find A's age.
A + B = 34
2A - B = 11
Adding the two equations: (A + B) + (2A - B) = 34 + 11
3A = 45
A = 15
Verification: B = 34 - 15 = 19
2(15) - 19 = 11 = 11 ✓

Question 14

The sum of A and B's ages is 49. Twice A's age minus B's age is 11. Find A's age.
A + B = 49
2A - B = 11
Adding the two equations: (A + B) + (2A - B) = 49 + 11
3A = 60
A = 20
Verification: B = 49 - 20 = 29
2(20) - 29 = 11 = 11 ✓

Question 15

The sum of A and B's ages is 59. Twice A's age minus B's age is 16. Find A's age.
A + B = 59
2A - B = 16
Adding the two equations: (A + B) + (2A - B) = 59 + 16
3A = 75
A = 25
Verification: B = 59 - 25 = 34
2(25) - 34 = 16 = 16 ✓

Question 16

The sum of A and B's ages is 38. Twice A's age minus B's age is 7. Find A's age.
A + B = 38
2A - B = 7
Adding the two equations: (A + B) + (2A - B) = 38 + 7
3A = 45
A = 15
Verification: B = 38 - 15 = 23
2(15) - 23 = 7 = 7 ✓

Question 17

The sum of A and B's ages is 53. Twice A's age minus B's age is 25. Find A's age.
A + B = 53
2A - B = 25
Adding the two equations: (A + B) + (2A - B) = 53 + 25
3A = 78
A = 26
Verification: B = 53 - 26 = 27
2(26) - 27 = 25 = 25 ✓

Question 18

The sum of A and B's ages is 41. Twice A's age minus B's age is 7. Find A's age.
A + B = 41
2A - B = 7
Adding the two equations: (A + B) + (2A - B) = 41 + 7
3A = 48
A = 16
Verification: B = 41 - 16 = 25
2(16) - 25 = 7 = 7 ✓

Question 19

The sum of A and B's ages is 56. Twice A's age minus B's age is 7. Find A's age.
A + B = 56
2A - B = 7
Adding the two equations: (A + B) + (2A - B) = 56 + 7
3A = 63
A = 21
Verification: B = 56 - 21 = 35
2(21) - 35 = 7 = 7 ✓

Question 20

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 ✓
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