Question 548945
The formula for simple interest is
{{{ A = P*( 1 + t*r ) }}}
{{{ A }}} = amount after {{{t}}} years
{{{ P }}} = original amount
{{{ r }}} = annual % interest rate
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Let the equation for the 1st loan be
{{{ A[1] = P[1]*( 1 + t*r[1] ) }}}
Let the equation for the 2nd loan be
{{{ A[2] = P[2]*( 1 + t*r[2] ) }}}
given:
{{{ r[1] = .063 }}}
{{{ r[2] = .088 }}}
{{{ P[1] + P[2] = 191610 }}}
and
Adding the 2 equations with {{{ t = 1 }}}
{{{ A[1] + A[2] = P[1] + P[1]*r[1] + P[2] + P[2]*r[2] }}}
{{{ A[1] + A[2] = 191610 + .063P[1] + .088P[2] }}}
The combined interest payment is
(1) {{{ .063P[1] + .088P[2] = 16681.66 }}}
But also
(2) {{{ P[1] + P[2] = 191610 }}}
Multiply both sides of (2) by {{{ .063 }}}
and subtract (2) from (1)
(1) {{{ .063P[1] + .088P[2] = 16681.66 }}}
(2) {{{-.063P[1] - .063P[2] = -12071.43 }}}
{{{ .025P[2] = 4610.23 }}}
{{{ P[2] = 184409.2 }}}
and, 
(2) {{{ P[1] + 184409.2 = 191610 }}}
(2) {{{ P[1] = 191610 - 184409.2 }}}
(2) {{{ P[1] = 7200.8 }}}
The amounts of the loans were:
$7,200.80 @ 6.3%
$184,409.20 @ 8.8%
check:
{{{ A[1] = P[1]*( 1 + .063 ) }}} ( {{{t}}} = 1 )
{{{ A[2] = P[2]*( 1 + .088 ) }}}
{{{ A[1] = 7200.8*( 1 + .063 ) }}} 
{{{ A[2] = 184409.2*( 1 + .088 ) }}}
{{{ A[1] = 7654.45 }}}
{{{ A[2] = 200637.21 }}}
The combined interest payment should be
{{{ A[1] + A[2] - (P[1] + P[2] )
{{{7654.45 + 200637.21 - 191610 }}}
{{{ 208291.66 - 191610 }}}
{{{ 16681.66 }}} This is correct