College algebra word problem

Question

A retired woman has $80,000 to invest but needs to make $9,000 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%.

Set up and solve the equation for how much the woman should invest in each option to sustain exactly a $9,000 annual return.

Answer 1

Hello, thank you for taking the time to post your question!

The key on this type of question is that you want to use the information given in order to set up an algebraic expression that relates the variables with one another. In this scenario that means

B + C = 80000   because she is investing a total of $80,000 in the bond (B) and cd (C)

0.15B + 0.07C = 9000   because the bond pays 15%, the cd pays 7%, and she needs to earn a total of $9000 in interest

I would plug in the first equation to the second equation using substitution and then solve for the value of B directly! When I do that I end up getting

B = 42500, meaning that C = 80000 – 42500 = 37500

So the end conclusion here is that the woman should invest $42,500 in the bond and $37,500 in the CD

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

She wants 9K interest on 80K, that's 11 1/4 % interest

Divide 9K by 80K or just 9/80 = 0.1125 = 11.25%

11.25 is slightly closer to 15 than to 7, so expect slightly more invested at 15%

15X + 7(80K-X) = 11.25(80K) = 900K

15X +560K- 7X = 900K

8X = 340K

X = 340K/8 = 42.5K = $42,500 at 15%

80K-X = 80K-42.5K = 37.5K = $37,500 at 7%