An investor has $1100 income from bonds bearing 4% and 5%. If the amounts at 4% and 5% were interchanged, she would earn $50 more per year. Find the total sum invested.

So, let's set this up:

0.04x+0.05y=1100
0.05x+0.04y=1150

Let's multiply each equation by 100:
4x+5y=110000
5x+4y=115000

Now let's add those together:

9x+9y=225000

And we need to find x+y, so we just divide by 9 and get 25,000