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
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 = 401. Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?
4. If 2x + 2(4 + 3x) < 2 + 3x > 2x + $\frac{x}{2}$; then x can take which of the following values?
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