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Master Equation System (Olympiad) - Beginner Level Problems Equation System (Olympiad) BEGINNER

Excel in competitive exams with this skill builder ⚡ worksheet on Equation System (Olympiad). Worksheet 3 of 10 contains 20 beginner-level problems. Target your step-by-step problem solving skills while practicing equation system (olympiad) practice, equation system (olympiad) for competitive exams, and how to solve equation system (olympiad).

📝 Worksheet 3 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner level

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Worksheet 3 of 10 (22% 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 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 3

The sum of A and B's ages is 35. Twice A's age minus B's age is 22. Find A's age.
A + B = 35
2A - B = 22
Adding the two equations: (A + B) + (2A - B) = 35 + 22
3A = 57
A = 19
Verification: B = 35 - 19 = 16
2(19) - 16 = 22 = 22 ✓

Question 4

The sum of A and B's ages is 30. Twice A's age minus B's age is 18. Find A's age.
A + B = 30
2A - B = 18
Adding the two equations: (A + B) + (2A - B) = 30 + 18
3A = 48
A = 16
Verification: B = 30 - 16 = 14
2(16) - 14 = 18 = 18 ✓

Question 5

The sum of A and B's ages is 33. Twice A's age minus B's age is 12. Find A's age.
A + B = 33
2A - B = 12
Adding the two equations: (A + B) + (2A - B) = 33 + 12
3A = 45
A = 15
Verification: B = 33 - 15 = 18
2(15) - 18 = 12 = 12 ✓

Question 6

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 7

The sum of A and B's ages is 42. Twice A's age minus B's age is 6. Find A's age.
A + B = 42
2A - B = 6
Adding the two equations: (A + B) + (2A - B) = 42 + 6
3A = 48
A = 16
Verification: B = 42 - 16 = 26
2(16) - 26 = 6 = 6 ✓

Question 8

The sum of A and B's ages is 47. Twice A's age minus B's age is 13. Find A's age.
A + B = 47
2A - B = 13
Adding the two equations: (A + B) + (2A - B) = 47 + 13
3A = 60
A = 20
Verification: B = 47 - 20 = 27
2(20) - 27 = 13 = 13 ✓

Question 9

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 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 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 12

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 13

The sum of A and B's ages is 34. Twice A's age minus B's age is 5. Find A's age.
A + B = 34
2A - B = 5
Adding the two equations: (A + B) + (2A - B) = 34 + 5
3A = 39
A = 13
Verification: B = 34 - 13 = 21
2(13) - 21 = 5 = 5 ✓

Question 14

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 15

The sum of A and B's ages is 31. Twice A's age minus B's age is 20. Find A's age.
A + B = 31
2A - B = 20
Adding the two equations: (A + B) + (2A - B) = 31 + 20
3A = 51
A = 17
Verification: B = 31 - 17 = 14
2(17) - 14 = 20 = 20 ✓

Question 16

The sum of A and B's ages is 36. Twice A's age minus B's age is 6. Find A's age.
A + B = 36
2A - B = 6
Adding the two equations: (A + B) + (2A - B) = 36 + 6
3A = 42
A = 14
Verification: B = 36 - 14 = 22
2(14) - 22 = 6 = 6 ✓

Question 17

The sum of A and B's ages is 49. Twice A's age minus B's age is 5. Find A's age.
A + B = 49
2A - B = 5
Adding the two equations: (A + B) + (2A - B) = 49 + 5
3A = 54
A = 18
Verification: B = 49 - 18 = 31
2(18) - 31 = 5 = 5 ✓

Question 18

The sum of A and B's ages is 35. Twice A's age minus B's age is 16. Find A's age.
A + B = 35
2A - B = 16
Adding the two equations: (A + B) + (2A - B) = 35 + 16
3A = 51
A = 17
Verification: B = 35 - 17 = 18
2(17) - 18 = 16 = 16 ✓

Question 19

The sum of A and B's ages is 36. Twice A's age minus B's age is 6. Find A's age.
A + B = 36
2A - B = 6
Adding the two equations: (A + B) + (2A - B) = 36 + 6
3A = 42
A = 14
Verification: B = 36 - 14 = 22
2(14) - 22 = 6 = 6 ✓

Question 20

The sum of A and B's ages is 42. Twice A's age minus B's age is 18. Find A's age.
A + B = 42
2A - B = 18
Adding the two equations: (A + B) + (2A - B) = 42 + 18
3A = 60
A = 20
Verification: B = 42 - 20 = 22
2(20) - 22 = 18 = 18 ✓
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