From the question
The sum of two investments = $9500
Let one of the investments be $x and the other be $y
Therefore
[tex]x+y=9500--------1[/tex]Peter lost 3 % on one and earned 7 % on the other
Therefore, we say
He lost 3% on $x
That is He lost $0.03x and
He earned 7% on $y
That is He earned $0.07y
Since his net annual receipts were $169
Then we have
[tex]-0.03x+0.07y=169--------2[/tex]Now we have to solve the equations simultaneously
From the first equation
[tex]x=9500-y------3[/tex]Substitute for x into equation 2
This gives
[tex]-0.03(9500-y)+0.07y=169[/tex]By solving for y we get
[tex]\begin{gathered} -285+0.03y+0.07y=169 \\ -285+0.1y=169 \\ 0.1y=169+285 \\ 0.1y=454 \\ y=\frac{454}{0.1} \\ y=4540 \end{gathered}[/tex]Substitute the value of y into equation 3
This gives
[tex]\begin{gathered} x=9500-4540 \\ x=4960 \end{gathered}[/tex]Therefore,
Each investment is
$4960 at 3% loss
$4540 at 7% profit