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Equation System (Olympiad) Beginner-Intermediate Worksheet: Focus on common variations practice Equation System (Olympiad) BEGINNER INTERMEDIATE

Level up your Equation System (Olympiad) skills! You're at Worksheet 4 of 10 (33% through this series). This step-up challenge worksheet features 20 beginner-intermediate-level problems with a focus on common variations practice. Topics covered: equation system (olympiad) for competitive exams, how to solve equation system (olympiad), equation system (olympiad) tricks.

📝 Worksheet 4 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner Intermediate level

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Worksheet 4 of 10 (33% complete)

Question 1

The sum of A and B's ages is 54. Twice A's age minus B's age is 15. Find A's age.
A + B = 54
2A - B = 15
Adding the two equations: (A + B) + (2A - B) = 54 + 15
3A = 69
A = 23
Verification: B = 54 - 23 = 31
2(23) - 31 = 15 = 15 ✓

Question 2

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 3

The sum of A and B's ages is 35. Twice A's age minus B's age is 19. Find A's age.
A + B = 35
2A - B = 19
Adding the two equations: (A + B) + (2A - B) = 35 + 19
3A = 54
A = 18
Verification: B = 35 - 18 = 17
2(18) - 17 = 19 = 19 ✓

Question 4

The sum of A and B's ages is 60. Twice A's age minus B's age is 9. Find A's age.
A + B = 60
2A - B = 9
Adding the two equations: (A + B) + (2A - B) = 60 + 9
3A = 69
A = 23
Verification: B = 60 - 23 = 37
2(23) - 37 = 9 = 9 ✓

Question 5

The sum of A and B's ages is 42. Twice A's age minus B's age is 12. Find A's age.
A + B = 42
2A - B = 12
Adding the two equations: (A + B) + (2A - B) = 42 + 12
3A = 54
A = 18
Verification: B = 42 - 18 = 24
2(18) - 24 = 12 = 12 ✓

Question 6

The sum of A and B's ages is 31. Twice A's age minus B's age is 5. Find A's age.
A + B = 31
2A - B = 5
Adding the two equations: (A + B) + (2A - B) = 31 + 5
3A = 36
A = 12
Verification: B = 31 - 12 = 19
2(12) - 19 = 5 = 5 ✓

Question 7

The sum of A and B's ages is 46. Twice A's age minus B's age is 11. Find A's age.
A + B = 46
2A - B = 11
Adding the two equations: (A + B) + (2A - B) = 46 + 11
3A = 57
A = 19
Verification: B = 46 - 19 = 27
2(19) - 27 = 11 = 11 ✓

Question 8

The sum of A and B's ages is 40. Twice A's age minus B's age is 14. Find A's age.
A + B = 40
2A - B = 14
Adding the two equations: (A + B) + (2A - B) = 40 + 14
3A = 54
A = 18
Verification: B = 40 - 18 = 22
2(18) - 22 = 14 = 14 ✓

Question 9

The sum of A and B's ages is 37. Twice A's age minus B's age is 17. Find A's age.
A + B = 37
2A - B = 17
Adding the two equations: (A + B) + (2A - B) = 37 + 17
3A = 54
A = 18
Verification: B = 37 - 18 = 19
2(18) - 19 = 17 = 17 ✓

Question 10

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 11

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 12

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 13

The sum of A and B's ages is 38. Twice A's age minus B's age is 13. Find A's age.
A + B = 38
2A - B = 13
Adding the two equations: (A + B) + (2A - B) = 38 + 13
3A = 51
A = 17
Verification: B = 38 - 17 = 21
2(17) - 21 = 13 = 13 ✓

Question 14

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 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 54. Twice A's age minus B's age is 18. Find A's age.
A + B = 54
2A - B = 18
Adding the two equations: (A + B) + (2A - B) = 54 + 18
3A = 72
A = 24
Verification: B = 54 - 24 = 30
2(24) - 30 = 18 = 18 ✓

Question 17

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 18

The sum of A and B's ages is 60. Twice A's age minus B's age is 24. Find A's age.
A + B = 60
2A - B = 24
Adding the two equations: (A + B) + (2A - B) = 60 + 24
3A = 84
A = 28
Verification: B = 60 - 28 = 32
2(28) - 32 = 24 = 24 ✓

Question 19

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 20

The sum of A and B's ages is 32. Twice A's age minus B's age is 13. Find A's age.
A + B = 32
2A - B = 13
Adding the two equations: (A + B) + (2A - B) = 32 + 13
3A = 45
A = 15
Verification: B = 32 - 15 = 17
2(15) - 17 = 13 = 13 ✓
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