Borrowing Money

A furniture borrowed $650,000 to expand it's store. Some money was borrowed at 4%, some at 6.5% and the rest at 9%. How much was borrowed at each rate if the annual interest was $46,250 and the amount borrowed at 9% was twice the amount borrowed at 4%.

What I get is: x@4%; y@6.5%; z@9%

x+y+z=650,000 BUT should it be -x-y-z=650,000 or x+y+z=650,000 ? I'm only asking because I've never seen a problem like this where money was borrowed and not invested.

What I have so far is:

x+y+z=650,000 (or some variation)
.04x+.065y+.09z =$46,250
2x +     z     = 0

(where z=2x)
so...
[1    1    1   650,000]
[.04 .065 .09  46,250]
[2    0    1   0]

then...
[1 0 0 -53,333.333]
[0 1 0  596666.666]
[0 0 1  106666.666]

But if I consider that it's borrowed then the x, y, z values of the first row should all be negative, right?

In this case I get:
[1 0 0  -1180000]
[0 1 0  -1830000]
[0 0 1   2,360,000]

What am I doing wrong? Am I just over thinking it.

Thanks

i did
[1.00 1.00 1.00 650000]
[0.04 .065 0.09 46359 ]
[2.00 0.00 -1.0 0     ]

and got
<x,y,z> = <164360, 156920, 328720>

your 2x + z = 0 shouldve been 2x - z = 0, since you're using the equation 2x = z
your other equations were fine

this is no different from an investment problem, you can phrase it as

"someone invests 650000 dollars, some at 4%, some at 6.5% and some at 9% interest, they receive 46359 in interest at the end of the year, and the amount they invested at 9% is twice the amount they invested at 4%"