Answer:
$2400 in A rated bond and $3000 in B rated bond.
Step-by-step explanation:
We have been given that Maria has recently retired and requested an extra $444.00 per year in income.
We can represent this information in an equation as:
[tex]A+B=5400...(1)[/tex]
She has $5400 to invest in an A-rated bond that pays 10% per annum or a B-rated bond paying 6% per annum.
[tex]0.10A+0.06B=444...(2)[/tex]
From equation (1), we will get:
[tex]A=5400-B[/tex]
Substitute this value in equation (2):
[tex]0.10(5400-B)+0.06B=444[/tex]
[tex]540-0.10B+0.06B=444[/tex]
[tex]540-0.04B=444[/tex]
[tex]540-540-0.04B=444-540[/tex]
[tex]-0.04B=-96[/tex]
[tex]\frac{-0.04B}{-0.04}=\frac{-96}{-0.04}[/tex]
[tex]A=2400[/tex]
Therefore, Maria should invest $2400 in A-rated bond.
Substitute [tex]A=2400[/tex] in equation (1):
[tex]2400+B=5400[/tex]
[tex]2400-2400+B=5400-2400[/tex]
[tex]B=3,000[/tex]
Therefore, Maria should invest $3000 in B-rated bond.
