Question 1080259
{{{ I = P*r*t }}} ( simple interest )
Let {{{ a }}} = amount invested @ 3%
{{{ 45000 - a }}} = amount invested @ 6.5%
Let {{{ b }}} = earnings from the 3% investment
{{{ 1980 - b }}} = earnings from the 6.5% investment
{{{ t = 1 }}} yr
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(1) {{{ b = a*.03*1 }}}
(2) {{{ 1980 - b = ( 45000 - a )*.065*1 }}}
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(1) {{{ b = .03a }}}
and
(2) {{{ 1980 - b = 2925 - .065a }}}
(2) {{{ b = .065a - 945 }}}
Plug (1) into (2)
(2) {{{ .03a = .065a - 945 }}}
(2) {{{ .035a = 945 }}}
(2) {{{ a = 27000 }}}
and
{{{ 45000 - a = 45000 - 27000 }}}
{{{ 45000 - a = 18000 }}}
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$27,000 @ 3%
$18,000 @ 6.5%
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check:
(1) {{{ b = a*.03*1 }}}
(1) {{{ b = 27000*.03*1 }}}
(1) {{{ b = 810 }}}
and
(2) {{{ 1980 - b = ( 45000 - a )*.065*1 }}}
(2) {{{ 1980 - b = 18000*.065*1 }}}
(2) {{{ 1980 - b = 1170 }}}
(2) {{{ b = 810 }}}
OK