Question 180998
Let {{{a}}} = amount invested @ 7%
Let {{{b}}} = amount invested @ 9%
given:
(1) {{{.07a + .09b = 970}}}
(2) {{{a + b = 12000}}}
Multiply both sides of (2) by {{{.07}}}
and subtract from (1)
(1) {{{.07a + .09b = 970}}}
(2) {{{-.07a - .07b = .07*12000}}}
And, subtracting:
(1) {{{.07a + .09b = 970}}}
(2) {{{-.07a - .07b = -840}}}
{{{.02b = 130}}}
{{{b = 6500}}}
And, since
(2) {{{a + b = 12000}}}
{{{a = 12000 - 6500}}}
{{{a = 5500}}}
$5500 was invested @ 7%
check:
(1) {{{.07a + .09b = 970}}}
{{{.07*5500 + .09*6500 = 970}}}
{{{385 + 585 = 970}}}
{{{970 = 970}}}
OK