Use the information given to set up equations as follows:

Assign variables: Let x be the amount invested in stocks, y the amount invested in bonds, and z the amount invested in money markets.

(1) The total amount invested is 100,000 which is the sum of the amounts invested:

x+y+z=100,000

(2) The total amount of income from the investments is 15,000. This is the sum of the incomes from the three investments. Since stocks earn 18% the income from stocks is .18x; similarly the income from bonds is .12y and from money markets is .06z.

So .18x+.12y+.06z=15,000 Multiplying through by 100 (to ease computations) we get:

18x+12y+6z=1,500,000

Now divide by 6:

3x+2y+z=250,000

(3) The amount invested in stocks is to be the sum of the amount invested in bonds and three times the amount invested in money markets. So x=y+3z. Rewriting in standard form we get:

x-y-3z=0

The system of equations:

x+y+z=100,000

3x+2y+z=250,000

x-y-3z=0

There are a number of methods to solve this system. Using Gaussian elimination we get:

`([1,1,1,|,100000],[3,2,1,|,250000],[1,-1,-3,|,0])==>([1,0,-1,|,50000],[0,1,2,|,50000],[0,0,0,|,0])`

The last row of zeros indicates that the system is dependent (there are many solutions.)

We see that x-z=50000 and y+2z=50000. Letting z be the independent variable the solutions can be described as:

(50000+z, 50000-2z, z)

For example we can let z=10,000; then x=60,000 and y=30,000. Note that the sum is 100,000 and .18x+.12y+06z=15,000.

Another choice might be z=20,000; then x=70,000 and y=10,000.

**Further Reading**