SOLUTION: Maricopa's Success scholarship fund receives a gift of $ 100000. The money is invested in stocks, bonds, and CDs. CDs pay 4.75 % interest, bonds pay 5.5 % interest, and stocks pay

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Question 1210274: Maricopa's Success scholarship fund receives a gift of $ 100000. The money is invested in stocks, bonds, and CDs. CDs pay 4.75 % interest, bonds pay 5.5 % interest, and stocks pay 6.7 % interest. Maricopa Success invests $ 40000 more in bonds than in CDs. If the annual income from the investments is $ 5590 , how much was invested in each account?
Found 3 solutions by Edwin McCravy, ikleyn, mccravyedwin:
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!



Solve the system and get

B=$60000, C = $20000, and S=$20000.

Here's an online solver to solve it for you so you don't have to do anything: 

https://www.emathhelp.net/calculators/algebra-2/system-of-equations-solver/

Edwin
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Maricopa's Success scholarship fund receives a gift of $100,000.
The money is invested in stocks, bonds, and CDs.
CDs pay 4.75 % interest, bonds pay 5.5 % interest, and stocks pay 6.7 % interest.
Maricopa Success invests $40,000 more in bonds than in CDs.
If the annual income from the investments is $5,590 , how much was invested in each account?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~


        This problem is very special. It asks about three unknowns,  but can be easily reduced
        to one single equation in one unknown.

        So,  to get the finish and the answer,  you don't need to write and to solve system of three
        linear equations.  Respectively,  using this approach,  you don't need to know the methods
        of solving systems of equation. 


Let x be the amount invested in CDs, in dollars.

Then the amount invested in bonds is (x+40,000) dollars.


Then the amount invested in stocks is  (100,000 - x - (x+40,000)) = (60000-2x).



Now, write this equation for the total annual interest

    0.0475x + 0.055*(x+40000) + 0.067*(60000-2x) = 5590  dollars.



Simplify it step by step and find x

    0.0475x + 0.055x + 2200 + 4020 - 0.134x = 5590,

    0.0475x + 0.055x - 0.134x = 5590 - 2200 - 4020,

    -0.0315x = -630

         x =  = 20000.


So, $20,000 were invested in CDs;  $20,000 + $40,000 = $60,000 were invested in bonds;  

and the rest, #100,000 - $20,000 - 60,000 = $20,000 were invested in stocks.

At this point, the problem is solved completely using one equation in one unknown.

In my solution,  I even did not pronounce these words  " system of equations ".


---------------------------


This approach teaches students to solve such problems in  3  (three)  unknowns in early age.

So,  it develops their mind,  which is a major goal of mathematical education.



Answer by mccravyedwin(407)   (Show Source): You can put this solution on YOUR website!
But the most efficient way is to translate each of the three sentences into
equations verbatim and use a solver.  These days, humans do the translating and
technology does the manipulating.  Math has changed.

Edwin
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