Question

I have $6400 to invest at 8% and 6%. What amount is to be invested at 8% in order to earn double the interest of 6%

Answer 1

Let x be the amount invested at 8%.
6400-x = amount invested at 6%.

Assuming simple interest, or invested for a short time, then

x*8% = 2(6400-x)*6%

Solve for x.

Answer 2

x = amount invested at 6%
y = amount invested at 8%
0.06x = interest at 0.06
0.08y = interest at 0.08

Solve simultaneously,
x + y = 6400
0.08y = 2(0.06x)

x = $2560
y = $3840
$153.60 = 6% int
$307.20 = 8% int