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Equation System (Olympiad): Worksheet 6 - Intermediate-Advanced Practice Equation System (Olympiad) INTERMEDIATE ADVANCED

Ready to master Equation System (Olympiad)? This timed practice ⚡ worksheet (6/10) presents 20 intermediate-advanced-level challenges. Focus area: speed building. Learn to solve equation system (olympiad) tricks, handle equation system (olympiad) shortcut methods, and perfect equation system (olympiad) bank exam questions with our step-by-step solutions.

📝 Worksheet 6 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate Advanced level

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Worksheet 6 of 10 (55% complete)

Question 1

The sum of A and B's ages is 46. Twice A's age minus B's age is 17. Find A's age.
A + B = 46
2A - B = 17
Adding the two equations: (A + B) + (2A - B) = 46 + 17
3A = 63
A = 21
Verification: B = 46 - 21 = 25
2(21) - 25 = 17 = 17 ✓

Question 2

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 ✓

Question 3

The sum of A and B's ages is 57. Twice A's age minus B's age is 24. Find A's age.
A + B = 57
2A - B = 24
Adding the two equations: (A + B) + (2A - B) = 57 + 24
3A = 81
A = 27
Verification: B = 57 - 27 = 30
2(27) - 30 = 24 = 24 ✓

Question 4

The sum of A and B's ages is 33. Twice A's age minus B's age is 21. Find A's age.
A + B = 33
2A - B = 21
Adding the two equations: (A + B) + (2A - B) = 33 + 21
3A = 54
A = 18
Verification: B = 33 - 18 = 15
2(18) - 15 = 21 = 21 ✓

Question 5

The sum of A and B's ages is 59. Twice A's age minus B's age is 7. Find A's age.
A + B = 59
2A - B = 7
Adding the two equations: (A + B) + (2A - B) = 59 + 7
3A = 66
A = 22
Verification: B = 59 - 22 = 37
2(22) - 37 = 7 = 7 ✓

Question 6

The sum of A and B's ages is 59. Twice A's age minus B's age is 22. Find A's age.
A + B = 59
2A - B = 22
Adding the two equations: (A + B) + (2A - B) = 59 + 22
3A = 81
A = 27
Verification: B = 59 - 27 = 32
2(27) - 32 = 22 = 22 ✓

Question 7

The sum of A and B's ages is 55. Twice A's age minus B's age is 17. Find A's age.
A + B = 55
2A - B = 17
Adding the two equations: (A + B) + (2A - B) = 55 + 17
3A = 72
A = 24
Verification: B = 55 - 24 = 31
2(24) - 31 = 17 = 17 ✓

Question 8

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 9

The sum of A and B's ages is 56. Twice A's age minus B's age is 16. Find A's age.
A + B = 56
2A - B = 16
Adding the two equations: (A + B) + (2A - B) = 56 + 16
3A = 72
A = 24
Verification: B = 56 - 24 = 32
2(24) - 32 = 16 = 16 ✓

Question 10

The sum of A and B's ages is 34. Twice A's age minus B's age is 14. Find A's age.
A + B = 34
2A - B = 14
Adding the two equations: (A + B) + (2A - B) = 34 + 14
3A = 48
A = 16
Verification: B = 34 - 16 = 18
2(16) - 18 = 14 = 14 ✓

Question 11

The sum of A and B's ages is 35. Twice A's age minus B's age is 7. Find A's age.
A + B = 35
2A - B = 7
Adding the two equations: (A + B) + (2A - B) = 35 + 7
3A = 42
A = 14
Verification: B = 35 - 14 = 21
2(14) - 21 = 7 = 7 ✓

Question 12

The sum of A and B's ages is 32. Twice A's age minus B's age is 25. Find A's age.
A + B = 32
2A - B = 25
Adding the two equations: (A + B) + (2A - B) = 32 + 25
3A = 57
A = 19
Verification: B = 32 - 19 = 13
2(19) - 13 = 25 = 25 ✓

Question 13

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 14

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 15

The sum of A and B's ages is 54. Twice A's age minus B's age is 6. Find A's age.
A + B = 54
2A - B = 6
Adding the two equations: (A + B) + (2A - B) = 54 + 6
3A = 60
A = 20
Verification: B = 54 - 20 = 34
2(20) - 34 = 6 = 6 ✓

Question 16

The sum of A and B's ages is 45. Twice A's age minus B's age is 6. Find A's age.
A + B = 45
2A - B = 6
Adding the two equations: (A + B) + (2A - B) = 45 + 6
3A = 51
A = 17
Verification: B = 45 - 17 = 28
2(17) - 28 = 6 = 6 ✓

Question 17

The sum of A and B's ages is 45. Twice A's age minus B's age is 12. Find A's age.
A + B = 45
2A - B = 12
Adding the two equations: (A + B) + (2A - B) = 45 + 12
3A = 57
A = 19
Verification: B = 45 - 19 = 26
2(19) - 26 = 12 = 12 ✓

Question 18

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 19

The sum of A and B's ages is 40. Twice A's age minus B's age is 11. Find A's age.
A + B = 40
2A - B = 11
Adding the two equations: (A + B) + (2A - B) = 40 + 11
3A = 51
A = 17
Verification: B = 40 - 17 = 23
2(17) - 23 = 11 = 11 ✓

Question 20

The sum of A and B's ages is 46. Twice A's age minus B's age is 17. Find A's age.
A + B = 46
2A - B = 17
Adding the two equations: (A + B) + (2A - B) = 46 + 17
3A = 63
A = 21
Verification: B = 46 - 21 = 25
2(21) - 25 = 17 = 17 ✓
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