10. 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

Answer: (If your answer isn't a positive integer, which it should be, then go check all your previous answers)

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Quiz Answer Key and Fun Facts

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

Answer: 18

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

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

Answer: 51

[(2b)/3] - 17 = b - 34
=> (2b)/3 - b = -34 + 17
=> (2b - 3b)/3 = -17
=> -b/3 = -17
=> -b = -17 * 3
=> b = 51

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

Answer: 12

12c - 2(c + 1) = 8c + 22
=> 12c - 2c - 2 = 8c + 22
=> 12c - 2c - 8c = 22 + 2
=> 2c = 24
=> c = 24/2
=> c = 12

4. If 3d - 5 = [(4d)/3] + 40, then the value of 'd' is...

Answer: 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

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

Answer: 3

(7e + 5)/e = 26/3
=> 21e + 15 = 26e
=> 26e - 21e = 15
=> 5e = 15
=> e = 15/5
=> e = 3

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

Answer: 2

(9 + 3f)/(4f + 22) = 1/2
=> 18 + 6f = 4f + 22
=> 6f - 4f = 22 - 18
=> 2f = 4
=> f = 4/2
=> f = 2

7. If (1 - 3g)/5 = -(g - 5), then the value of 'g' is...

Answer: 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

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

Answer: 6

9h - 4 = (16h + 4)/2
=> 18h - 8 = 16h + 4
=> 18h - 16h = 4 + 8
=> 2h = 12
=> h = 12/2
=> h = 6

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

Answer: 12

(4i - 8)/5 = i - 4
=> 4i - 8 = 5i - 20
=> 5i - 4i = 20 - 8
=> i = 12

Answer: 5

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)!

Source: Author achernar

This quiz was reviewed by FunTrivia editor CellarDoor before going online.
Any errors found in FunTrivia content are routinely corrected through our feedback system.

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