Answer
The answer is: one part gets $\mathsf{$}$375, the second part gets $\mathsf{$}$125 and the third part gets $\mathsf{$}$500.
Work Step by Step
Assign the variables:
x = first part
y = second part
z = third part
$\textbf{Step 1:}$
Find the equations that represent the problem.
We know that $x+y+z=1000$, because the addition of the three parts has to equal the total amount of dollars.
$x+y+z=1000$ $\leftarrow$ Eq. 1
We can get the second equation from the wording in the problem.
From "one part will be three times as large as the second ", we get
$x=3y$ $\leftarrow$ Eq. 2
We can get the third equation from the wording in the problem.
From " the third part will be as large as the sum of the other two", we get
$z=x+y$ $ \leftarrow$ Eq. 3
$\textbf{Step 2:}$
Solve the system of equations. Using the substitution method,
a) Substitute Eq. 3 into Eq. 1
$z+z=1000$
$2z=1000$
$z=\frac{1000}{2}$
$z=500$
b) Substitute Eq. 2 and the value for $z$ into Eq. 3
$500=3y+y$
$500=4y$
$y=\frac{500}{4}$
$y=125$
c) Substitute the value for $y$ into Eq. 2
$x=3(125)$
$x=375$
$\textbf{Step 3:}$
The answer is: one part gets $\mathsf{$}$375, the second part gets $\mathsf{$}$125 and the third part gets $\mathsf{$}$500.
