Question 1204756
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An investor has $50,000 to invest in three types of bonds: short-term, intermediate-term, 
and long-term. How much should she invest in each type to satisfy the given conditions?
Short-term bonds pay 4% annually, intermediate-term bonds pay 5%, and long-term bonds pay 6%. 
The investor wishes to realize a total annual income of 5.22%, with equal amounts 
invested in short- and intermediate-term bonds.
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x dollars invested in short-term  (4% annually);

x dollars invested in intermediate-term  (5% annually);

the rest (50000-2x) dollars invested in long-term  (6% annually).


Now write the total annual interest equation

    0.04x + 0.05x + 0.06(50000-2x) = 0.0522*50000.


Simplify step by step and find x

    0.04x + 0.05x - 0.06*(2x) = 0.0522*50000 - 0.06*50000

    (0.04 + 0.05 -  0.12)x = -390

            -0.03x         = -390

                 x         = 390/0.03 = 13,000.


<U>ANSWER</U>.  Invest $13,000 in short-term;  $13,000 in intermediate-term;  the resr 50000-13000-13000 = 24000 in long-term.


<U>CHACK</U>.  0.04*13000 + 0.05*13000 + 0.06*24000 = 2610 dollars, total annual interest.

        0.0522*50000 = 2610 dollars,  the same amount.   ! solved correctly !
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Solved


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;using one single unknown and one single equation.