Question 1068523
This looks like a simple interest problem
I can use:
{{{ I = P*r*t }}} where
{{{ I }}} = interest after {{{ t }}} years
{{{ P }}} = amount invested
{{{ r }}} = interest rate
{{{ t }}} = years invested
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{{{ I[1] = P[1]*r[1]*t }}}
(1) {{{ I[1] = P[1]*.04*1 }}}
(1) {{{ P[1] = 25I[1] }}}
and
{{{ I[2] = P[2]*r[2]*t }}}
(2) {{{ 50 - I[1] = ( 1000 - P[1] )*.065*1 }}}
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(2) {{{ 50 - I[1] = 65 - .065P[1] }}}
(2) {{{ I[1] = .065P[1] - 15 }}}
Substitute (1) into (2)
(2) {{{ I[1] = .065*25*I[1] - 15 }}}
(2) {{{ I[1] = 1.625I[1] - 15 }}}
(2) {{{ .625I[1] = 15 }}}
(2) {{{ I[1] = 24 }}}
and
(2) {{{ I[2] = 50 - I[1] }}}
(2) {{{ I[2] = 50 - 24 }}}
(2) {{{ I[2] = 26 }}}
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(1) {{{ P[1] = 25I[1] }}}
(1) {{{ P[1] = 25*24 }}}
(1) {{{ P[1] = 600 }}}
and
{{{ I[2] = P[2]*.065*1 }}}
{{{ 26 = P[2]*.065 }}}
{{{ P[2] = 26/.065 }}}
{{{ P[2] = 400 }}}
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$600 was invested @ 4%
$400 was invested @ 6.5%
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check:
{{{ P[1] + P[2] = 1000 }}}
{{{ 600 + 400 = 1000 }}}
and
{{{ I[1] + I[2] = 50 }}}
{{{ 24 + 26 = 50 }}}
OK