Question 439570
Let {{{a}}} = amount invested @ 3% interest
Let {{{b}}} = amount invested @ 4% interest
given:
(1) {{{ a + b = 12000 }}}
(2) {{{ .03a + .04b = 440 }}}
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(2) {{{ .03a + .04b = 440 }}}
(2) {{{ 3a + 4b = 44000 }}}
Multiply both sides of (1) by {{{3}}}
and subtract (1) from (2)
(2) {{{ 3a + 4b = 44000 }}}
(1) {{{ -3a - 3b = -36000 }}}
{{{ b = 8000 }}}
and, since
(1) {{{ a + b = 12000 }}}
(1) {{{ a + 8000 = 12000 }}}
{{{ a = 4000 }}}
$4,000 = amount invested @ 3% interest
$8,000 = amount invested @ 4% interest
check answer:
(2) {{{ .03a + .04b = 440 }}}
(2) {{{ .03*4000 + .04*8000 = 440 }}}
{{{ 120 + 320 = 440 }}}
{{{ 440 = 440 }}}
OK