Question 1154741
(1) {{{ I[1] = P[1]*r[1]*t }}}
(2) {{{ I[2] = P[2]*r[2]*t }}}
{{{ r[1] = .06 }}}
{{{ r[2] = .12 }}}
{{{ P[2] = 5500 - P[1] }}}
{{{ t = 1 }}}
{{{ I[1] + I[2] = 522 }}}
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(1) {{{ I[1] = P[1]*.06*1 }}}
(2) {{{ 522 - I[1] = ( 5500 - P[1] )* .12*1 }}}
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(2) {{{ 522 - I[1] = 660 - .12P[1] }}}
(2) {{{ I[1] = .12P[1] - 138 }}}
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Plug (1) into (2) 
(2) {{{ .06P[1] = .12P[1] - 138 }}}
(2) {{{ .06P[1] = 138 }}}
(2) {{{ P[1] = 2300 }}}
and
{{{ P[2] = 5500 - P[1] }}}
{{{ P[2] = 5500 - 2300 }}}
{{{ P[2] = 3200 }}}
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$2,300 @ 6%
$3,200 @ 12%
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check:
(1) {{{ I[1] = 2300*.06*1 }}}
(1) {{{ I[1] = 138 }}}
{{{ I[2] = 522 - I[1] }}}
{{{ I[2] = 522 - 138 }}}
{{{ I[2] = 384 }}}
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(2) {{{ 522 - I[1] = ( 5500 - P[1] )* .12*1 }}}
(2) {{{ 522 - 138 = ( 5500 - P[1] )* .12*1 }}}
(2) {{{ 384 = 3200*.12 }}}
(2) {{{ 384 = 384 }}}
OK