You invest in AAA-rated bonds, A-rated bonds, and B-rated bonds. The average yields are 4.5% on AAA

Question:

You invest in AAA-rated bonds, A-rated bonds, and B-rated bonds. The average yields are 4.5% on AAA bonds, 5% on A bonds, and 9% on B bonds. You invest 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.

z = (total investment) y + 0.045x + 0.05y + 0.09z = (annual return) 2y –

Use the inverse of the coefficient matrix of this system to find the amount invested in each type of bond for the given total investment and annual return.
Total Investment.................................................. Annual Return
$10,000 ............................................................. $650