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8 August, 08:25

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?

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  1. 8 August, 09:45
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    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
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