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 = 51000 because she is investing a total of $51,000 between the two bonds
0.01x + 0.08y = 2890 because the first bond pays 1%, the second bond pays 8%, and she needs to earn a total of $2890 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 = 34000, meaning that x = 51000 – 34000 = 17000
So the end conclusion here is that the woman should invest $17,000 in the 1% bond and $34,000 in the 8% bond
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 :)
