Betsy, a recent  retiree, requires $6,000 per year in extra income. she has 70,000 to invest and can invest in  b-rated bonds paying 13% per year or in a certificate of deposit  (cd) paying 5% per year. how much money should be invested in each to realize exactly 6,000 in interest per  year?

Let x represent the amount invested at the higher rate. Then 70,000-x is the amount invested at the lower rate. The interest earned is ...

... 0.13x + 0.05(70000-x) = 6000

... 0.08x + 3500 = 6000 . . . . . . . . . simplify

... .08x = 2500 . . . . . . . . . . . . . . . . . subtract 3500

... x = 2500/0.08 = 31250 . . . . . . . .divide by .08

Betsy should invest $31,250 at 13% and $38,750 at 5%.

answer: x=60