Question 102343
First Part + Second Part + Third Part = 1000
First Part = 3 x Second Part
Third Part = First Part + Second Part

Let's assign a variable to each part.
X = First Part
Y = Second Part
Z = Third Part

{{{X + Y + Z = 1000}}} Your original equation. 
{{{X = 3*Y}}} First Part = 3 x Second Part
{{{Z = X + Y = (3*Y) + Y = 4Y}}}Third Part = First Part + Second Part
{{{X + Y + Z = 1000}}}
{{{3*Y + Y + 4*Y = 1000}}} Substitute for what you know, in terms of Y. \
{{{8*Y = 1000}}} Simplify. 
{{{cross(8)Y/cross(8) = 1000/8}}} Use multiplicative inverse of 8. 
{{{Y = 125}}}
{{{X = 3*Y = 3*(125) = 375}}}
{{{Z = X + Y = 125 + 375 = 500}}}
So then,
First Part = 125
Second Part = 375 
Third Part = 500