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Of the three numbers the sum of first two is 55, the sum of the second and the third is 75 and the sum of the third and thrice the first is 100. Determine the third number.

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Of the three numbers the sum of first two is 55, the sum of the second and the third is 75 and the sum of the third and thrice the first is 100. Determine the third number.
1). 30
2). 20
3). 35
4). 40


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Answered by on | Votes 1 |

Let the three numbers be ‘x’, ‘y’ and ‘z’.

Given, x + y = 55; y + z = 75 and z + 3x = 100

Let the above three equations be (1), (2) and (3) respectively.

From equation (1), y = 55 – x and From (3), z = 100 – 3x

Substituting in (2) ⇒ 55 – x + 100 – 3x = 75

⇒ 155 – 4x = 75 ⇒ 155 – 75 = 4x ⇒ 80 = 4x ⇒ x = 80/4 = 20

⇒ z = 100 – 3 × 20 = 100 – 60 = 40

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