Question 28285
After you've done enough of these interest and other types of word problems
you get a sense of where to start. 
As soon as I saw that they're doing 2 different things with $5000 what popped
into my head was x and 5000 - x 
This is a great way to divide 5000 in two, the sum adds up to 5000 as it should
and your unknown is neatly tucked into each part. Very useful
What do you do with it?
Let x be the amount invested at 12%
So the rest of the $5000, namely 5000 - x, is invested at 9%
Following the problem, 
{{{.12 * x = .09 * (5000 - x) + 348.75}}}
Solve for x
{{{.12 * x = 450 - .09 * x  + 348.75}}}
{{{.21 * x = 450 + 348.75}}}
{{{.21 * x = 798.75}}}
I get
x = 3803.60
and
5000 - x = 1196.40
Those would be the amounts invested at 12% and 9%
checking
{{{.12 * 3803.60 = .09 * 1196.40  + 348.75}}}
{{{456.43 = 107.68 + 348.75}}}
{{{456.43 = 456.43}}}
Unless I goofed that's it