How much did he invest in each account?

Question

Dan had
$20,000
to invest. He invested some of it in an account that paid
7%
simple interest per year, and he invested the rest in an account that paid
8%
simple interest per year. After one year, he received a total of
$1470
in interest. How much did he invest in each account?

Answer 1

I would set this up as a very simple matrix.

 

First, let x = $ amount invested at 7%

        let y = $ amount invested at 8%

 

Develop equations from what we know:

 

$20,000 invested between those 2 percentage rates.  So:  x + y =20,000

$  1,470 of interest earned between amounts invested at those 2 percentage rates.  So:  0.07x + 0.08y = 1,470

 

From this, we can develop the following tableau for Iteration 0:

 

1          1          =          20000

0.07     0.08      =            1470

 

We want to isolate so that we have 1x and 1y.  To do this, we do row operations.  The first row operation is:  -7R1 + 100R2 = new R2; which gives us the new matrix iteration of:

 

1          1          =          20000

0          1          =            7000

 

We want to get the R1,C2 value to also become 0.  So, we do the 2nd row operation of:  -R2 + R1 = new R1; which gives us the new matrix iteration of:

 

1          0          =          13000

0          1          =            7000

 

This gives us (x, y) of (13000, 7000); which means:

 

$13,000 invested at 7%; $7,000 invested at 8%

 

Next, we test our answers back into the 2 original equations:

 

(1)  x + y = 20,000; 13,000 + 7,000 = 20,000    [Check]

(2)  0.07x + 0.08y = 1,470; 0.07 * 13,000 + 0.08 * 7,000 = 1,470     [Check]