Question 542392
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.