Question 115895
Let's call the amount at 4%, F, and at 12%, T. 
Here's what you know. 
1.{{{F+T=20000}}} Total is $20,000.
Gain is positive interest, loss is negative interest. 
2.{{{-0.04F+0.12T=0}}} Interest from both broke even (totaled zero). 
Let solve equation 2 for F in terms of T. 
2.{{{-0.04F+0.12T=0}}} 
{{{-0.04F=-0.12T}}} 
{{{F=0.12T/0.04}}} 
{{{F=3T}}} 
Now substitute that value in equation 1 and solve for T.
1.{{{F+T=20000}}}
{{{3T+T=20000}}}
{{{4T=20000}}}
{{{T=5000}}}
and 
{{{F=3T}}}
{{{F=3(5000)}}}
{{{F=15000}}}
Check the answers
1. Total is $20,000
2. Loss at 4% = (0.04)(15,000) = -6,000
Gain at 12% = (0.12)(5,000) = 6,000
Sum is zero. 
Good answers.
$5,000 at 4% and $15,000 at 12%.