Question 13261
Let x = the amount invested the mutual fund @ 4% per annum.
Then $270,000.00 - x is invested in the "junk" bonds @ 8% per annum.
Since the annual interest is the same for both of these investments, then you can write:

{{{0.04x = (0.08)(270000 - x)}}} Simplify and solve for x.
{{{0.04x = 21600 - 0.08x}}} Add 0.08x to both sides.
{{{0.12x = 216000}}} Divide both sides by 0.12
{{{x = 180000}}}

The retiree has $180,000.00 invested in the mutual fund @ 4% per annum and 
$270,000.00 - $180,000.00 = $90,000.00 invested in "junk" bonds @ 8% per annum.