Question 1166329
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Edmonds Community College's (EDCC) scholarship fund received a gift of $ 110,000.
The money is invested in stocks, bonds, and CDs.
CDs pay 5.25% interest, bonds pay 5% interest, and stocks pay 10.8% simple interest.
EDCC invests $ 10,000 more in bonds than in CDs.
If the annual income from the investments is $7,328 , how much was invested in each vehicle?
solve by the method of your choice either using reduced row echelon form or the matrix equation
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        This problem can be solved by much more intelligent way by reducing it to a single 

        equation for only one unknown, as I will show below in my post.



<pre>
Let x be the amount invested in CDs, in dollars.

Then the amount invested in bonds is (x+10000) dollars,

and the amount invested in stocks is the rest  (110000 - x - (x+10000)) = (100000-2x)  dollars.


Now write an equation for the total interest from three investments

    0.0525x + 0.05*(x+10000) + 0.108*(100000-2x) = 7328  dollars.


Simplify and find x

    0.0525x + 0.05x + 500 + 10800 - 0.216x = 7328

    (0.0525 + 0.05 - 0.216)x = 7328 - 500 - 10800

            -0.1135x         =      -3972

                   x         =       3972/0.1135 = 34995.60


Thus, $34995.60                       invested in CDs,  

      $34995.60 + $10000 = $44995.60 invested in bonds,

      and the rest,  (110000 - 34995.60 - 44995.60) = 30008.80 dollars invested in stocks.
</pre>

Solved.


Compare this simple treatment with megaton calculations in the other post.


Simply and elegantly - - - as it should be in true Math.


If you never saw this approach before, it is a good time for you  
to learn it now and to take it into service.