Question 111578
First, let's name the variables.
E=amount borrowed at 8%
N=amount borrowed at 9%
T=amount borrowed at 10%
Next, let's write down what you know.
1.Amount Borrowed : {{{E+N+T=800000}}}
2.Total Interest :{{{ 0.08*E+0.09N+0.10*T=67000}}}
3.Relationship between E and T : {{{E=5T}}}
Let's substitute equation 3 into equations 1 and 2.
1.  {{{E+N+T=800000}}}
1.  {{{5T+N+T=800000}}}
1.  {{{N+6T=800000}}}
2. {{{ 0.08*E+0.09N+0.10*T=67000}}}
2. {{{ 8E+9N+10T=6700000}}}
2. {{{ 8(5T)+9N+10T=6700000}}}
2. {{{ 9N+50T=6700000}}}
Now let's use equation 1 and solve for N in terms of T. 
1.  {{{N+6T=800000}}}
1.  {{{N=800000-6T}}}
We can substitute that result into 2 and solve for T.
2. {{{ 9N+50T=6700000}}}
{{{ 9(800000-6T)+50T=6700000}}}
{{{ 7200000-54T+50T=6700000}}}
{{{ 7200000-4T=6700000}}}
{{{ -4T=6700000-7200000}}}
{{{ -4T=-500000}}}
{{{ T=125000}}}
From 1,
1.  {{{N=800000-6T}}}
{{{N=800000-6(125000)}}}
{{{N=50000}}}
and from 3,
{{{E=5T}}}
{{{E=5(125000)}}}
{{{E=625000}}}
Let's check the answers.
{{{E+N+T=800000}}}
{{{625000+50000+125000=800000}}}
{{{800000=800000}}}
True statement.
{{{ 0.08*E+0.09N+0.10*T=67000}}}
{{{0.08(625000)+0.09(50000)+0.10(125000)=67000}}}
{{{50000+4500+12500=67000}}}
{{{67000=67000}}}
True statement.
Your answers led to true statement. 
They're good answers. 
$625,000 borrowed at 8%
$50,000 borrowed at 9%
$125,000 borrowed at 10%