5000 is invested at 3 percent interest. how much money must be invested at 5 percent interest so that the total interest from the two investments is 275 after one year

Whatever% of anything is just (whatever/100) * anything.

so, 5000 at 3% will just be (3/100) * 5000, or 150 bucks.

now, if the two investments were to yield 275, we know the first yields 150, so the second investment must yield the difference, or 275 - 150, or 125.

so, what's the Principal to be invested for 1 year at 5% to get 125 bucks in interest from it?

Here's the appropriate equation:

5000(0.03)(1) + x(0.05)(1) = 275

Then 150 + .05x = 275, or

                    0.05x = 125, or  x = 2500

Invest $2500 at 5% for one year.