Question 92

If $$2x(x+y+z)$$ = 250, $$2y(x+y+z)$$ = 100, $$2z(x+y+z)$$ = 100, then find the value of $$(3x+6y+15z)$$.

Solution

2x(x + y + z) = 250 ----(1)

2y(x + y + z) = 100 ----(2)

2z(x + y + z) = 100 ----(3)

Adding equation (1), (2) and (3)

⇒ (2x + 2y + 2z)(x + y + z) = 450

⇒ (x + y + z)(x + y + z) = 225

⇒ (x + y + z) = 15

⇒ x = 25/3, y = 10/3 and z = 10/3

∴ (3x + 6y + 15z) = 95

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