Question 509643
Let S = the total amount of Jolene's savings.
She invests two thirds of S in the bank that pays 3% interest and the remaining one third of S in the bank that pays 8% interest.
So we can write the equation that relates the interest amounts earned at each bank to the total amount of interest earned ($6,076).
{{{(2/3)S(0.03) + (1/3)S(0.08) = 6076}}} It will make the calculations a little easier if we change the interest rates to fractions.
{{{3}}}% = {{{0.03}}}={{{3/100}}} and {{{8}}}%={{{0.08 = 8/100}}}
{{{(2/3)S(3/100)+(1/3)S(8/100) = 6076}}} Now simplify the left side of the equation.
{{{2S/100 + 8S/300 = 6076}}} Add the fractions.
{{{(6S+8S)/300 = 6076}}} Simplify.
{{{14S/300 = 6076}}} Multiply both sides by 300.
{{{14S =  1822800}}} Divide both sides by 14.
{{{S = 130200}}}
Jolene's total invested savings is:
$130,200
Two thirds of this are invested at 3%, so...
{{{0.03(2/3)(130200) = (3/100)(2/3)(130200)}}}={{{(2/100)(130200) = 2604}}}
$2,604 interest was earned at 3% per annum.
One third of $130,200 was invested at 8%, so...
{{{0.8(1/3)(130200) = (8/100)(1/3)(130200))}}}={{{(8/300)(130200) = 3472}}}
$3,472 interest was earned at 8% per annum.
The the total interest is:
{{{2604+3472 = 6076}}} = $6,076