Consider a Person Who Invests in AAA-Rated Bonds,A-Rated Bonds,and B-Rated

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. Total Investment
Annual Return
$12,000
890 $$\left\{ \begin{array} { c l } x + y + z & = 12,000 \text { (total investment) } \\0.065 x + 0.07 y + 0.09 z & = 890 \text { (annual retum) } \\2 y - z & = 0\end{array} \right.$$ Use the inverse of the coefficient matrix of this system to find the amount invested in each type of bond.

A) $7,000 in AAA-rated bonds $2,000 in A-rated bonds
$4,000 in B-rated bonds
B) $5,000 in AAA-rated bonds $7,000 in A-rated bonds
$3,000 in B-rated bonds
C) $5,000 in AAA-rated bonds $6,000 in A-rated bonds
$4,000 in B-rated bonds
D) $3,000 in AAA-rated bonds $2,000 in A-rated bonds
$6,000 in B-rated bonds
E) $6,000 in AAA-rated bonds $2,000 in A-rated bonds
$4,000 in B-rated bonds