Question 495194
This looks like simple interest, and not compound interest
Let {{{a}}} = amount invested @ 4%
Let {{{b}}} = amount invested @ 3.5%
Let {{{c}}} = amount invested @ 3%
given:
(1) {{{ .04a + .035b + .03c = 416 }}}
(2) {{{ .04a = .035b + .03c + 104 }}}
(3) {{{ .045a + .04b + .035c = 471.75 }}}
---------------------------------
Multiply both sides of all equations by {{{ 1000 }}}
(1) {{{ 40a + 35b + 30c = 416000 }}}
(2) {{{ 40a = 35b + 30c + 104000 }}}
(3) {{{ 45a + 40b + 35c = 471750 }}}
-----------------------------
Divide both sides of all equations by {{{ 5 }}}
(1) {{{ 8a + 7b + 6c = 83200 }}}
(2) {{{ 8a = 7b + 6c + 20800 }}}
(3) {{{ 9a + 8b + 7c = 94350 }}}
--------------------------
Rewrite (2) and add it to (1)
(1) {{{ 8a + 7b + 6c = 83200 }}}
(2) {{{ 8a - 7b  - 6c = 20800 }}}
{{{ 16a = 104000 }}}
{{{ a = 6500 }}}
-------------
Put this value back into (1)
(1) {{{ 8*6500 + 7b + 6c = 83200 }}}
(1) {{{ 52000 + 7b + 6c = 83200 }}}
(1) {{{ 7b + 6c = 83200 - 52000 }}}
(1) {{{ 6c = 31200 - 7b }}}
{{{ c = 5200 - (7/6)*b }}}
---------------------
Plug this result into (3)
(3) {{{ 9a + 8b + 7c = 94350 }}}
(3) {{{ 9*6500 + 8b + 7*(5200 - (7/6)*b) = 94350 }}}
(3) {{{ 58500 + 8b + 36400 - 8.1666b = 94350 }}}
(3) {{{ .1666b = 58500 - 94350 + 36400 }}}
(3) {{{ .1666b = 550 }}}
{{{ b = 3300 }}}
-------------
Plug {{{a}}} and {{{b}}} into (1) to find {{{c}}}
(1) {{{ 8a + 7b + 6c = 83200 }}}
(1) {{{ 8*6500 + 7*3300 + 6c = 83200 }}}
(1) {{{ 52000 + 23100 + 6c = 83200 }}}
(1) {{{ 6c = 83200 - 75100 }}}
(1) {{{ 6c = 8100 }}}
{{{ c = 1350 }}}
-------------
$6,500 = amount invested @ 4%
$3,300 = amount invested @ 3.5%
$1,350 = amount invested @ 3%