Question 1205201
.
Mark has $100,000 to invest. His financial consultant advises him to diversify his investment 
in three types of bonds: short-term, intermediate-term, and long-term. 
The short-term bonds pay 4%, the intermediate-term bonds pay 5%, and the long-term bonds pay 6% 
simple interest per year. Mark wishes to realize a total annual income of 5.1%, 
with equal amounts invested in short- and intermediate-term bonds. How much should he invest in each type of bond?
short-term
intermediate-term
long-term
~~~~~~~~~~~~~~~~~~~~~~


<pre>
x = short term;

x = intermediate term;

(100,000-2x) = long term.


Write the total annual interest equation

    0.04x + 0.05x + 0.06*(100000-2x) = 0.051*100000.


Simplify this equation and find x

    0.04x + 0.05x - 0.06*(2x) + 6000 = 5100

          -0.03x                      = 5100 - 6000

          -0.03x                     =    -900

                x                     = {{{(-900)/(-0.03)}}} = 30000.


<U>ANSWER</U>.  $30,000 = short term;  $30,000 = intermediate term;  $100,000 - $30,000 - $30,000 = $40,000 = long term.
</pre>

Solved.


Notice that three unknowns are found using one equation in one unknown.