Ms. Blackmon invested $8000, part at 4% and the rest at 5% per year. How much did she invest at each rate if her total return per year on the investments was $380?

Question

anonymous · Answer

Let x = the part at 4% and y the part at 5%.
x(1.04)+y(1.05)=8380
x+y=8000
y=8000-x
.04x+.05y=380
.04x+.05(8000-x)=380
.04x+400-.05x=380
-.01x=-20
x=2000
this implies that y = 6000

anonymous · Answer

Not sure I understand how you did that, how did you come up with the x(1.04) + y(1.05) = 8380?

anonymous · Answer

Are you still there?

anonymous · Answer

if you leave it collecting interest for one period of interest (a year) then the amount that is collecting interest (the amounts x and y, both components of the 8000) collect 1+the % of interest.  So...for the x amount 1.04x, and the y amount follows.  It should follow naturally that the two amounts, increased by interest, should equal the original total plus the interest (380).  Let me know if I still haven't cleared it up

anonymous · Answer

Oh good grief, you just added the interest of 380 to the 8000 total
lol   I'm sorry, I'm an idiot.....