Question 1109146
Let {{{ a }}} = amount invested @ 5%
Let {{{ b }}} = amount invested @ 6%
Let {{{ c }}} = amount invested @ 6.5%
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(1) {{{ I[a] = P[a]*.05*1 }}}
(2) {{{ I[b] = P[b]*.06*1 }}}
(3) {{{ I[c] = P[c] *.065*1}}}
(4) {{{ I[a] + I[b] + I[c] = 1170 }}}
(5) {{{ P[a] + P[b] + P[c] = 20000 }}}
(6) {{{ 3P[b] = P[a] + P[c] }}}
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There are 6 equations and 6 unknowns,
so it's solvable
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Plug (6) into (5)
(5) {{{ P[b] + 3P[b] = 20000 }}}
(5) {{{ 4P[b] = 20000 }}}
(5) {{{ P[b] = 5000 }}}
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Plug this result into (2)
(2) {{{ I[b] = 5000*.06 }}}
(2) {{{ I[b] = 300 }}}
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Plug this result back into (6)
(6) {{{ P[a] + P[c] = 15000 }}}
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and from (1), (2), and (3)
{{{ .05P[a] + .06P[b] + .065P[c] = 1170 }}}
{{{ 50P[a] + 60P[b] + 65P[c] = 1170000 }}}
{{{ 10P[a] + 12P[b] + 13P[c] = 234000 }}}
{{{ 10P[a] + 12*5000 + 13P[c] = 234000 }}} 
{{{ 10P[a] + 13P[c] = 234000 - 60000 }}}
{{{ 10P[a] + 13P[c] = 174000 }}}
Multiply both sides of (6) by {{{ 10 }}}
and subtract (6) from this result
{{{ 10P[a] + 13P[c] = 174000 }}}
{{{ -10P[a] - 10P[c] = -150000 }}}
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{{{ 3P[c] = 24000 }}}
{{{ P[c] = 8000 }}}
and
(5) {{{ P[a] + P[b] + P[c] = 20000 }}}
(5) {{{ P[a] + 5000 + 8000 = 20000 }}}
(5) {{{ P[a] = 7000 }}}
I think you can finish from here
Definitely check the math.
I think the method good, though