A retired woman has $90,000 to invest but needs to make $3,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%. If we let x be the amount the woman invests in the 15% bond, how much in dollars will she be able to invest in the CD?

see below

Step-by-step explanation:

$3000 is not a right number or $90000

Assume n instead of $3000, then

x*0.15 + (90000-x) * 0.07 = n

is required equation

0.15x+6300-0.07x=n 0.08x+6300=n 0.08x = n-6300

x = (n-6300) / 0.08 is the amount invested in the 15% bond

Consider n> $6300

Then 90000 - x will be the amount invested in the CD

Answer: any amount from 0 to 90000 USD

Step-by-step explanation:

x USD will be paid for 15% bonds that makes x*0.15 USD / per year

So 90000-x will be paid for 7% bonds, that makes (90000-x) * 0.07 USD/per year = 6300-0.07x USD / per year.

So the total amount the woman gets from both investments yearly should be not less than 3000 USD/per year

Otherwise

0.15*x+6300-0.07*x>=3000

0.08*x+6300>=3000

The inequation is correct for any x>=0

The woman will be able invest in CD any amount from 0 to 90000 USD.

If we suppose that investments in CD more safe we'd recommend to the lady to invest all money to CD.