Question below.

Question

Jim invested 14 000 in stocks and bonds. The stocks earned interest at a rate of 8% per year, whereas the bonds earned 6%. The total amount earned was 1000, how much was earned by bonds and stocks?

Answer 1

This is a matrix problem:

 

Let x = amount invested in stocks

Let y = amount invested in bonds

 

We know that the total amount invested was $14,000    [x + y = 14000]

 

We also know that the stocks returned 8%, while the bonds returned 6%, with the total returned of $1,000 [0.08x + 0.06y = 1000]

 

That gives us the following matrix setup:

 

1          1          =          14000

0.08      0.06     =            1000

 

I wish to get rid of the value in R2, C1 first.  So, I do this by:

 

-2R1 + 25R2  = new R2    , which gives us:

 

1.00          1.00          =          14000

0.00         -0.50          =          -3000

 

Then, I wish to get rid of the value in R1, C2 second.  So, I do this by:

 

2R2 + R1 = new R1      , which gives us:

 

1.00        0.00       =           8000

0.00       -0.50       =         -3000

 

Next, I want the value in R2, C2, to be 1.00.  I do this by multiplying:

 

-2R1 = new R1       , which gives us:

 

1          0           =          8000

0          1           =          6000

 

So, x=8000; y=6000

 

This mean, therefore, that $8,000 was invested in stocks; $6,000 invested in bonds.