Math Solution with Explanation (Math Problem Sample)

A retired couple has $160,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 6%. The rest they want to invest in AA bonds yielding 11% per year. How much should they invest in each to realize exactly $15,600 per year?
SOLUTION WITH EXPLANATION
To give a solution this problem we take a given amount to be invested in AA bonds to be of unknown value y, obtaining a interest of 11% (0.11) ,thus the amount left after investing in AA bonds given by (160000-y) will be invested in safe certificate of deposit yielding with interest of 6%(0.06) .
Recall that the total interest is equal to 15600
Interest from AA bonds is given by: % interest*amount invested, 0.11*y = 0.11y
Interest from safe certificate of deposit yielding is given by: % interest*amount invested, 0.06*(160000-y) = 0.11y
Therefore 0.11y + (160000-y) 0.06 = 15600
0.11y + 9600 -0.06y =