Anna asks her broker to divide her investment of $2000 among three funds, x, y, and z. she decides that her investment in x should be twice her investment in z. during the first quarter, x earned 4.5%, y earned 2.6%, and z lost 0.2%. anna earned $58 on her investment during that period. how many dollars did the broker put into each fund?

Answer: X=1200, Y=200, Z=600

Given: X+Y+Z=2000

X=2Z

2Z+Y+Z=2000

Y=2000-3z

During the first quarter=

X (4.5%) + (2000-3z) (2.6%) + z (-.2%) = 58

2z (4.5%) + (2000-3z) (2.6%) + z (-.2%) = 58

2z (.045) + (2000-3z) (.026) -.002z=58

.09z+52-.078z-.002z=58

.01z=58-52

Z=6/.01

Z=600

X = 2z

X=2 (600)

X=1200

If X+y+z=2000

Y=2000-600-1200

Y=200

To counter check:

X (4.5%) + (2000-3z) (2.6%) + z (-.2%) =

1200 (.045) + 200 (.026) - 600 (.002) =

54+5.2 - 1.2=58