Consider a Person Who Invests in AAA-Rated Bonds,A-Rated Bonds,and B-Rated $$\begin{array} { | c | c | } \hline \text { Total Investment } & \text { Annual Return } \\\hline \$ 12,000 & 890 \\\hline\end{array}$$

Consider a person who invests in AAA-rated bonds,A-rated bonds,and B-rated bonds.The average yields are 6.5% on AAA bonds,7% on A bonds,and 9% on B bonds.The person invests twice as much in B bonds as in A bonds.Let x,y and z represent the amounts invested in AAA,A,and B bonds,respectively. $$\begin{array} { | c | c | } \hline \text { Total Investment } & \text { Annual Return } \\\hline \$ 12,000 & 890 \\\hline\end{array}$$ $$\left\{ \begin{array} { c l } x + y + z & = 663,000 \text { (total investment) } \\0.065 x + 0.07 y + 0.09 z & = 47,000 \text { (annual retum) } \\2 y - z & = 0\end{array} \right.$$ Use the inverse of the coefficient matrix of this system to find the amount invested in each type of bond.
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A) $142,000 in AAA-rated bonds $451,000 in A-rated bonds
$71,000 in B-rated bonds
B) $450,000 in AAA-rated bonds $71,000 in A-rated bonds
$142,000 in B-rated bonds
C) $143,000 in AAA-rated bonds $71,000 in A-rated bonds
$450,000 in B-rated bonds
D) $72,000 in AAA-rated bonds $450,000 in A-rated bonds
$142,000 in B-rated bonds
E) $450,000 in AAA-rated bonds $142,000 in A-rated bonds
$70,000 in B-rated bonds