Question 132062
Jane invested 
${{{a}}} at 12%
${{{b}}} at 10%
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Randy invested
${{{b}}} at 12%
${{{a}}} at 10%
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For Jane:
(1) {{{.12a + .1b = 130}}}
For Randy:
(2) {{{.12b + .1a = 134}}}
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Rewrite (2) as:
{{{.12b + .1a = 130 + 4}}}
(3) {{{.12b + .1a - 4 = 130}}}
Set the left side of (3) equal to the left
side of (1)
{{{.12b + .1a - 4 = .12a + .1b}}}
{{{.02b - .02a = 4}}}
divide both sides by {{{.02}}}
{{{b - a = 200}}}
{{{b = 200 + a}}}
Substitute this in (1)
{{{.12a + .1(200 + a) = 130}}}
{{{.12a + 20 + .1a = 130}}}
{{{.22a = 110}}}
{{{a = 500}}}
{{{b = 200 + a}}}
{{{b = 700}}}
Jane invested 
${{{500}}} at 12%
${{{700}}} at 10%
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Randy invested
${{{700}}} at 12%
${{{500}}} at 10%
check answers:
(1) {{{.12a + .1b = 130}}}
{{{.12*500 + .1*700 = 130}}}
{{{60 + 70 = 130}}}
{{{130 = 130}}}
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(2) {{{.12b + .1a = 134}}}
{{{.12*700 + .1*500 = 134}}}
{{{84 + 50 = 134}}}
{{{134 = 134}}}
OK