If 2x(x + y + z) = 250, 2y(x + y + z) = 100, 2z(x + y + z) = 100, then find the value of (3x + 6y + 15z).
95
Add the three given equations: $2x(x+y+z) + 2y(x+y+z) + 2z(x+y+z) = 250 + 100 + 100$, so $2(x+y+z)^2 = 450$, giving $(x+y+z)^2 = 225$ and $x+y+z = 15$.
Substitute $x+y+z = 15$ back: $2x \times 15 = 250 \Rightarrow x = 25/3$; $2y \times 15 = 100 \Rightarrow y = 10/3$; similarly $z = 10/3$.
Then $3x + 6y + 15z = 3(25/3) + 6(10/3) + 15(10/3) = 25 + 20 + 50 = 95$.
Hence, 95.
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