Question 542392: Ana Colon asks her broker to divide her 401k investment of $2000 among the International Fund, Fixed Assets Fund, and Company Stock. She decides her investment in the International Fund should be twice her investment in company stock. During the first quarter, the International Fund earns 4.5%, the Fixed Assets fund earns 2.6%, and the company stock drops .2%. At the end of the first quarter, Ms. Colon receives a statement indicating a return of $58 on her investment. How did the broker divide Ms. Colon's initial investment
the key
international is $1200
Fixed fund is $ 200
company is $ 600
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = investment in international fund.
let y = investment in fixed assets fund
let z = investment in company stock.
x = 2z (investment in international fund is twice investment in company stock).
your original equations are:
x + y + z = 2000 (total investment)
.045x + .026y - .002z = 58 (total interest on investment)
4.5% = .045
2.6% = .026
.2% = .002
you know that x = 2z, so you substitute in your original equations to get:
2z + y + z = 2000 (total investment)
.045(2z) + .026y - .002z = 58 (total interest on investment).
you combine like terms to get:
y + 3z = 2000
.026y +.088z = 58
these are 2 equations in 2 unknowns that need to be solved simultaneously.
if you multiply the first equation by (-.026), then you will get:
-.026y = -.078z = -52
.026y .088z = 58
if you add these 2 equations together, then you will get:
.01z = 6
if you divide both sides of this equation by .01, then you will get:
z = 600
now that you found z, you can solve for y.
in the equation y + 3z = 2000, substitute 600 for z to get:
y + 1800 = 2000
subtract 1800 from both sides of this equation to get:
y = 200
since x is equal to 2z (given), then:
x = 2 * 600 = 1200
your answer is:
x = 1200
y = 200
z = 600
that agrees with your key so the answer is correct.
international fund is 1200
fixed assets is 200
company fund is 600.
international fund is 2 times company fund.
the reason you multiplied your first equation by -.026 is so you could eliminate the y from the set of equations to get 2 equations in 2 unknowns which can be solved for an exact answer.
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