College algebra word problem

Question

Paul has $70,000 to invest. His intent is to earn 12% interest on his investment. He can invest part of his money at 8% interest and part at 13% interest. How much does Paul need to invest in each option to make a total 12% return on his $70,000?

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 we have

x + y = 70000 because he is investing a total of $70,000 between the two bonds

0.08x + 0.13y = 8400   because the first investment pays 8%, the second investment pays 13%, and he needs to earn a total of $8400 in interest

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

y = 56000, meaning that x = 70000 – 56000 = 14000

So the end conclusion here is that the woman should invest $14,000 in the 8% category and $56,000 in the 13% category in order to achieve a 12% return

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

13X + 8(70K-X) = 12(70K)

Let X = amount invested at 13%

70K-X= amount invested at 8%

K= $1000

13X+560K-8X = 840K

5X= (840-560)K = 280K

5X = 280K

X = 280K/5 = 56K = $56,000

70K-X = (70-56)K = 14K = $14,000

another way to approach it is

13-8 = 5, and 13-12 = 1

You want 1/5 of 70K = 14K for 8%

and 4/5 of 70K = 56K for 13%

13(4) + 1(8) =5(12)

52 + 8 = 60

You want 4 times as much 13% as 8% to get 12%