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Equation System (Olympiad) - Absolute-Beginner Level: core concept mastery Equation System (Olympiad) ABSOLUTE BEGINNER

This skill primer 🌟 worksheet focuses on Equation System (Olympiad) - a key topic in Age Problems. You'll solve 20 absolute-beginner-level problems (Worksheet 1 of 10). The primary focus is on core concept mastery. Master equation system (olympiad) problems, equation system (olympiad) reasoning questions, and equation system (olympiad) practice through systematic practice.

📝 Worksheet 1 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Absolute Beginner level

What you'll learn in this worksheet:
Your progress through Equation System (Olympiad)
Worksheet 1 of 10 (0% complete)

Question 1

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 2

The sum of A and B's ages is 60. Twice A's age minus B's age is 18. Find A's age.
A + B = 60
2A - B = 18
Adding the two equations: (A + B) + (2A - B) = 60 + 18
3A = 78
A = 26
Verification: B = 60 - 26 = 34
2(26) - 34 = 18 = 18 ✓

Question 3

The sum of A and B's ages is 38. Twice A's age minus B's age is 10. Find A's age.
A + B = 38
2A - B = 10
Adding the two equations: (A + B) + (2A - B) = 38 + 10
3A = 48
A = 16
Verification: B = 38 - 16 = 22
2(16) - 22 = 10 = 10 ✓

Question 4

The sum of A and B's ages is 31. Twice A's age minus B's age is 23. Find A's age.
A + B = 31
2A - B = 23
Adding the two equations: (A + B) + (2A - B) = 31 + 23
3A = 54
A = 18
Verification: B = 31 - 18 = 13
2(18) - 13 = 23 = 23 ✓

Question 5

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 6

The sum of A and B's ages is 49. Twice A's age minus B's age is 14. Find A's age.
A + B = 49
2A - B = 14
Adding the two equations: (A + B) + (2A - B) = 49 + 14
3A = 63
A = 21
Verification: B = 49 - 21 = 28
2(21) - 28 = 14 = 14 ✓

Question 7

The sum of A and B's ages is 59. Twice A's age minus B's age is 13. Find A's age.
A + B = 59
2A - B = 13
Adding the two equations: (A + B) + (2A - B) = 59 + 13
3A = 72
A = 24
Verification: B = 59 - 24 = 35
2(24) - 35 = 13 = 13 ✓

Question 8

The sum of A and B's ages is 31. Twice A's age minus B's age is 23. Find A's age.
A + B = 31
2A - B = 23
Adding the two equations: (A + B) + (2A - B) = 31 + 23
3A = 54
A = 18
Verification: B = 31 - 18 = 13
2(18) - 13 = 23 = 23 ✓

Question 9

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 10

The sum of A and B's ages is 47. Twice A's age minus B's age is 16. Find A's age.
A + B = 47
2A - B = 16
Adding the two equations: (A + B) + (2A - B) = 47 + 16
3A = 63
A = 21
Verification: B = 47 - 21 = 26
2(21) - 26 = 16 = 16 ✓

Question 11

The sum of A and B's ages is 55. Twice A's age minus B's age is 11. Find A's age.
A + B = 55
2A - B = 11
Adding the two equations: (A + B) + (2A - B) = 55 + 11
3A = 66
A = 22
Verification: B = 55 - 22 = 33
2(22) - 33 = 11 = 11 ✓

Question 12

The sum of A and B's ages is 47. Twice A's age minus B's age is 22. Find A's age.
A + B = 47
2A - B = 22
Adding the two equations: (A + B) + (2A - B) = 47 + 22
3A = 69
A = 23
Verification: B = 47 - 23 = 24
2(23) - 24 = 22 = 22 ✓

Question 13

The sum of A and B's ages is 38. Twice A's age minus B's age is 16. Find A's age.
A + B = 38
2A - B = 16
Adding the two equations: (A + B) + (2A - B) = 38 + 16
3A = 54
A = 18
Verification: B = 38 - 18 = 20
2(18) - 20 = 16 = 16 ✓

Question 14

The sum of A and B's ages is 58. Twice A's age minus B's age is 5. Find A's age.
A + B = 58
2A - B = 5
Adding the two equations: (A + B) + (2A - B) = 58 + 5
3A = 63
A = 21
Verification: B = 58 - 21 = 37
2(21) - 37 = 5 = 5 ✓

Question 15

The sum of A and B's ages is 35. Twice A's age minus B's age is 13. Find A's age.
A + B = 35
2A - B = 13
Adding the two equations: (A + B) + (2A - B) = 35 + 13
3A = 48
A = 16
Verification: B = 35 - 16 = 19
2(16) - 19 = 13 = 13 ✓

Question 16

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 17

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 18

The sum of A and B's ages is 37. Twice A's age minus B's age is 14. Find A's age.
A + B = 37
2A - B = 14
Adding the two equations: (A + B) + (2A - B) = 37 + 14
3A = 51
A = 17
Verification: B = 37 - 17 = 20
2(17) - 20 = 14 = 14 ✓

Question 19

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 20

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 ✓
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