You invest in AAA-rated bonds, A-rated bonds, and B-rated bonds. Your average yield is 8% on AAA bonds, 9% on A bonds, and 10% on B bonds. You invest twice as much in B bonds as in A bonds. The desired system of linear equations (where $x,$ $y,$ and $z$ represent the amounts invested in AAA, A, and B bonds, respectively) is as follows. $\left\{ \begin{aligned}
x + y + z & = ( \text { total investment) } \
0.08 x + 0.09 y + 0.1 z & = \text { (annual return) } \
2 y - z & = 0
\end{aligned} \right.$ Use the inverse of the coefficient matrix of this system to find the amount invested in B bonds for the given a total investment of $18,000 and annual return of $1640.
A)$8000
B)$6000
C)$9000
D)$1000
E)$2000

Question

Quizplus · Accepted Answer

The correct system of equations based on the given information is:$$x + y + z = 18000$$$$0.08x + 0.09y + 0.1z = 1640$$$$2y - z = 0$$To find the amount invested in B bonds ($z$), we solve the system using the inverse of the coefficient matrix. The solution involves matrix operations that lead to finding the values of $x$, $y$, and $z$. Given the specific details of the problem, the correct answer is found through these calculations, which indicate that the amount invested in B bonds is $8000.

You Invest in AAA-Rated Bonds, A-Rated Bonds, and B-Rated Bonds x,x,x,

You Invest in AAA-Rated Bonds, A-Rated Bonds, and B-Rated Bonds $x,$