Question 1066863
{{{ I[1] = P[1]*r[1]*t }}}
(1) {{{ I[1] = P[1]*.05*1 }}}
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{{{ I[2] = P[2]*r[2]*t }}}
(2) {{{ I[2] = P[2]*.08*1 }}}
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(3) {{{ I[1] + I[2] = 4650 }}}
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Now just swap the interest rates
{{{ I[1] = P[1]*r[2]*t }}}
(4) {{{ I[3] = P[1]*.08*1 }}}
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{{{ I[2] = P[2]*r[1]*t }}}
(5) {{{ I[4] = P[2]*.05*1 }}}
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(6) {{{ I[3] + I[4] = 5100 }}}
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(3) {{{ I[1] + I[2] = 4650 }}}
Use (1) and (2) to get:
(3) {{{ .05P[1] + .08P[2] = 4650 }}}
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(6) {{{ I[3] + I[4] = 5100 }}}
Use (4) and (5) to get:
(6) {{{ .08P[1] + .05P[2] = 5100 }}}
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(3) {{{ 5P[1] + 8P[2] = 465000 }}}
(6) {{{ 8P[1] + 5P[2] = 510000 }}}
Multiply both sides of (3) by {{{ 8 }}}
Multiply both sides of (6) by {{{ 5 }}}
Subtract (6) from (3)
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(3) {{{ 40P[1] + 64P[2] = 3720000 }}}
(6) {{{ -40P[1] - 25P[2] = -2550000 }}}
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{{{ 39P[2] = 1170000 }}}
{{{ P[2] = 30000 }}}
and
(3) {{{ 5P[1] + 8P[2] = 465000 }}}
(3) {{{ 5P[1] + 8*30000 = 465000 }}}
(3) {{{ 5P[1] = 465000 - 240000 }}}
(3) {{{ 5P[1] = 225000 }}}
(3) {{{ P[1] = 45000 }}}
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P 45,000 is invested @ 5%
P 30,000 is invested @ 8%
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check:
(1) {{{ I[1] = P[1]*.05*1 }}}
(1) {{{ I[1] = 45000*.05*1 }}}
(1) {{{ I[1] = 2250 }}}
and
(2) {{{ I[2] = P[2]*.08*1 }}}
(2) {{{ I[2] = 30000*.08*1 }}}
(2) {{{ I[2] = 2400 }}}
and
(3) {{{ I[1] + I[2] = 4650 }}}
(3) {{{ 2250 + 2400 = 4650 }}}
(3) {{{ 4650 = 4650 }}}
OK
You can check {{{ I[3] }}} and {{{ I[4] }}}
the same way