college algebra

Question

A combined total of $45,000 is invested in two bonds that pay 2% and 6.5% simple interest. The annual interest is $2,340.00. How much is invested in each bond?

The amount invested at 2% is $ .

The amount invested at 6.5% is $ .

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 = 45000 because they are investing a total of $45,000 between the two bonds

0.02x + 0.065y = 2340  because the first investment pays 2%, the second investment pays 6.5%, and they need to earn a total of $2340 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 = 32000, meaning that x = 45000 – 32000 = 13000

So the end conclusion here is that the woman should invest $13,000 in the 2% category and $32,000 in the 6.5% category in order to achieve the desired 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

X + y = 45000

0.02 x + 0.065 y = 2340

0.02x + 0.065 (45000 - x) = 2340

0.02x + 2925 - 0.065x = 2340

-0.045x = 2340-2925

-0.045x = -585

x = 13000

y = 32000