Question 1067791
Let {{{ P[1] }}} = amount invested @ 3%
{{{ P[2] = 15000 - P[1] }}} = amount invested @ 4.5%
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Use {{{ I = P*r*t }}}
{{{ t = 1 }}} yr
{{{ r[1] = .03 }}}
{{{ r[2] = .045 }}}
(1) {{{ I[1] + I[2] = 600 }}}
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{{{ I[1] = P[1]*r[1]*t }}}
{{{ I[1] = P[1]*.03*1 }}}
(2) {{{ I[1] = .03P[1] }}}
and
(3) {{{ I[2] = P[2]*.045*1 }}}
{{{ 600 - I[1] = .045*( 15000 - P[1] )
{{{ 600 - I[1] = 675 - .045*P[1] }}}
By substitution:
{{{ 600 - .03P[1] = 675 - .045*P[1] }}}
{{{ .015P[1] = 75 }}}
{{{ P[1] = 5000 }}}
and
{{{ P[2] = 15000 - P[1] }}}
{{{ P[2] = 15000 - 5000 }}}
{{{ P[2] = 10000 }}}
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$5,000 = amount invested @ 3%
$10,000 = amount invested @ 4.5%
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check:
(2) {{{ I[1] = .03P[1] }}}
(2) {{{ I[1] = .03*5000 }}}
(2) {{{ I[1] = 150 }}}
and
(3) {{{ I[2] = P[2]*.045*1 }}}
(3) {{{ I[2] = .045*10000 }}}
(3) {{{ I[2] = 450 }}}
and
(1) {{{ I[1] + I[2] = 600 }}}
(1) {{{ 150 + 450 = 600 }}}
(1) {{{ 600 = 600 }}}
OK