Question 880545
Let {{{ a }}} = amt invested @ 6%
Let {{{ b }}} = amt invested @ 8%
Let {{{ c }}} = amt invested @ 12%
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given:
(1) {{{ a + b + c = 75000 }}}
(2) {{{ b = 3c }}}
(3) {{{ .06a + .08b + .12c = 5700 }}}
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Substitute (2) into (1)
(1) {{{ a + 3c + c = 75000 }}}
(1) {{{ a = -4c + 75000 }}}
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Now substitute this result and (2) into (3)
(3) {{{ .06*( -4c + 75000 ) + .08*(3c) + .12c = 5700 }}}
(3) {{{ -.24c + 4500 + .24c + .12c = 5700 }}}
(3) {{{ .12c = 1200 }}}
(3) {{{ c = 10000 }}}
and, since
(2) {{{ b = 3c }}}
(2) {{{ b = 30000 }}}
and
(1) {{{ a + b + c = 75000 }}}
(1) {{{ a + 30000 + 10000 = 75000 }}}
(1) {{{ a = 75000 - 40000 }}}
(1) {{{ a = 35000 }}}
amt invested @ 6% is $35,000
amt invested @ 8% is $30,000
amt invested @ 12% is $10,000
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check:
(1) {{{ a + b + c = 75000 }}}
(1) {{{ 35000 + 30000 + 10000 = 75000 }}}
(1) {{{ 75000 = 75000 }}}
OK
(3) {{{ .06a + .08b + .12c = 5700 }}}
(3) {{{ .06*35000 + .08*30000 + .12*10000 = 5700 }}}
(3) {{{ 2100 + 2400 + 1200 = 5700 }}}
(3) {{{ 5700 = 5700 }}}
OK