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Master Equation System (Olympiad) - Intermediate-Advanced Level Problems Equation System (Olympiad) INTERMEDIATE ADVANCED

Excel in competitive exams with this self assessment worksheet on Equation System (Olympiad). Worksheet 7 of 10 contains 20 intermediate-advanced-level problems. Target your accuracy improvement skills while practicing equation system (olympiad) shortcut methods, equation system (olympiad) bank exam questions, and equation system (olympiad) ssc cgl.

📝 Worksheet 7 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate Advanced level

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Worksheet 7 of 10 (66% complete)

Question 1

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 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 30. Twice A's age minus B's age is 12. Find A's age.
A + B = 30
2A - B = 12
Adding the two equations: (A + B) + (2A - B) = 30 + 12
3A = 42
A = 14
Verification: B = 30 - 14 = 16
2(14) - 16 = 12 = 12 ✓

Question 4

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 5

The sum of A and B's ages is 52. Twice A's age minus B's age is 17. Find A's age.
A + B = 52
2A - B = 17
Adding the two equations: (A + B) + (2A - B) = 52 + 17
3A = 69
A = 23
Verification: B = 52 - 23 = 29
2(23) - 29 = 17 = 17 ✓

Question 6

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 7

The sum of A and B's ages is 60. Twice A's age minus B's age is 21. Find A's age.
A + B = 60
2A - B = 21
Adding the two equations: (A + B) + (2A - B) = 60 + 21
3A = 81
A = 27
Verification: B = 60 - 27 = 33
2(27) - 33 = 21 = 21 ✓

Question 8

The sum of A and B's ages is 46. Twice A's age minus B's age is 5. Find A's age.
A + B = 46
2A - B = 5
Adding the two equations: (A + B) + (2A - B) = 46 + 5
3A = 51
A = 17
Verification: B = 46 - 17 = 29
2(17) - 29 = 5 = 5 ✓

Question 9

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 10

The sum of A and B's ages is 30. Twice A's age minus B's age is 21. Find A's age.
A + B = 30
2A - B = 21
Adding the two equations: (A + B) + (2A - B) = 30 + 21
3A = 51
A = 17
Verification: B = 30 - 17 = 13
2(17) - 13 = 21 = 21 ✓

Question 11

The sum of A and B's ages is 50. Twice A's age minus B's age is 7. Find A's age.
A + B = 50
2A - B = 7
Adding the two equations: (A + B) + (2A - B) = 50 + 7
3A = 57
A = 19
Verification: B = 50 - 19 = 31
2(19) - 31 = 7 = 7 ✓

Question 12

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 13

The sum of A and B's ages is 52. Twice A's age minus B's age is 20. Find A's age.
A + B = 52
2A - B = 20
Adding the two equations: (A + B) + (2A - B) = 52 + 20
3A = 72
A = 24
Verification: B = 52 - 24 = 28
2(24) - 28 = 20 = 20 ✓

Question 14

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 15

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 16

The sum of A and B's ages is 37. Twice A's age minus B's age is 20. Find A's age.
A + B = 37
2A - B = 20
Adding the two equations: (A + B) + (2A - B) = 37 + 20
3A = 57
A = 19
Verification: B = 37 - 19 = 18
2(19) - 18 = 20 = 20 ✓

Question 17

The sum of A and B's ages is 58. Twice A's age minus B's age is 20. Find A's age.
A + B = 58
2A - B = 20
Adding the two equations: (A + B) + (2A - B) = 58 + 20
3A = 78
A = 26
Verification: B = 58 - 26 = 32
2(26) - 32 = 20 = 20 ✓

Question 18

The sum of A and B's ages is 46. Twice A's age minus B's age is 20. Find A's age.
A + B = 46
2A - B = 20
Adding the two equations: (A + B) + (2A - B) = 46 + 20
3A = 66
A = 22
Verification: B = 46 - 22 = 24
2(22) - 24 = 20 = 20 ✓

Question 19

The sum of A and B's ages is 52. Twice A's age minus B's age is 8. Find A's age.
A + B = 52
2A - B = 8
Adding the two equations: (A + B) + (2A - B) = 52 + 8
3A = 60
A = 20
Verification: B = 52 - 20 = 32
2(20) - 32 = 8 = 8 ✓

Question 20

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 ✓
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