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 Fun Trivia: A : Algebra

### Special Sub-Topic: Linear Equations in One Variable

 If a + 54 = 5a - 18, then the value of 'a' is...

18. a + 54 = 5a - 18 => 54 + 18 = 5a - a => 72 = 4a => a = 72/4 => a = 18

 If [(2b)/3] - 17 = b - 34, then the value of 'b' is...
51. [(2b)/3] - 17 = b - 34 => (2b)/3 - b = -34 + 17 => (2b - 3b)/3 = -17 => -b/3 = -17 => -b = -17 * 3 => b = 51

 If 12c - 2(c + 1) = 8c + 22, then the value of 'c' is...
12. 12c - 2(c + 1) = 8c + 22 => 12c - 2c - 2 = 8c + 22 => 12c - 2c - 8c = 22 + 2 => 2c = 24 => c = 24/2 => c = 12

 If 3d - 5 = [(4d)/3] + 40, then the value of 'd' is...
27. 3d - 5 = [(4d)/3] + 40 => 3d - (4d)/3 = 40 + 5 => (9d - 4d)/3 = 45 => (5d)/3 = 45 => 5d = 45 * 3 => 5d = 135 => d = 135/5 => d = 27

 If (7e + 5)/e = 26/3, then the value of 'e' is...
3. (7e + 5)/e = 26/3 => 21e + 15 = 26e => 26e - 21e = 15 => 5e = 15 => e = 15/5 => e = 3

 If (9 + 3f)/(4f + 22) = 1/2, then the value of 'f' is...
2. (9 + 3f)/(4f + 22) = 1/2 => 18 + 6f = 4f + 22 => 6f - 4f = 22 - 18 => 2f = 4 => f = 4/2 => f = 2

 If (1 - 3g)/5 = -(g - 5), then the value of 'g' is...
12. (1 - 3g)/5 = -(g - 5) => (1 - 3g)/5 = -g + 5 => 1 - 3g = -5g + 25 => -3g + 5g = 25 - 1 => 2g = 24 => g = 24/2 => g = 12

 If 9h - 4 = (16h + 4)/2, then the value of 'h' is...
6. 9h - 4 = (16h + 4)/2 => 18h - 8 = 16h + 4 => 18h - 16h = 4 + 8 => 2h = 12 => h = 12/2 => h = 6

 If (4i - 8)/5 = i - 4, then the value of 'i' is...
12. (4i - 8)/5 = i - 4 => 4i - 8 = 5i - 20 => 5i - 4i = 20 - 8 => i = 12

 Now, using the values for 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h' and 'i' which you have obtained from the equations in questions 1 - 9, find the value of 'x' in the following equation: [(b/e + x)/x][(fc - g)/i] = (d/x + a + e)/h
5 & five. From questions 1 to 9, the values for the all variables 'a' to 'i' that you get are: 'a'=18, 'b'=51, 'c'=12, 'd'=27, 'e'=3, 'f'=2, 'g'=12, 'h'=6, and 'i'=12. Now, by putting these values in the equation in the question, you get: [(51/3 + x)/x][(2 * 12 - 12)/12] = (27/x + 18 + 3)/6 => [(17 + x)/x][(24 - 12)/12] = (27/x + 21)/6 => [(17 + x)/x][12/12] = (27/x + 21)/6 => [(17 + x)/x] * 1 = (27/x + 21)/6 => (17 + x)/x = (27/x + 21)/6 => 102 + 6x = 27 + 21x => 21x - 6x = 102 - 27 => 15x = 75 => x = 75/15 => x = 5 Phew! I hope you enjoyed solving these equations (regardless of how well you did)!

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