College Algebra

Question

Scott invested a total of $9500 at two separate banks. One bank pays simple interest of 10 % per year while the other pays simple interest at a rate of 9 % per year. If Scott earned $ 914.00 in interest during a single year, how much did he have on deposit in each bank?

Answer 1

a + b = 9500 --------a = 9500 - b

10a + 9b = 91400 (multiplied by 100 to get rid of those pesky decimals)

 

10(9500 - b) + 9b = 91400

95000 - 10b + 9b = 91400

b = 3600

 

a = 9500 - 3600 = 5900

 

He deposited $5900 into bank A and $3600 into bank B.

Answer 2

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

The key on this type of question is finding a way to relate the variables to one another in an algebraic expression. On this one we have

x + y = 9500         because we know that he invested $9500 in total between the two assets

0.10x + 0.09y = 914    because between the 10% return and 9% return he earned $914 in total interest

I would substitute in the first expression into the second and then solve for the underlying value of “y” … when I do that I get y = 3600, meaning that x = 9500 – 3600 = 5900

So he invested $5,900 at the 10% rate and then the remaining $3,600 at the 9% rate

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 :)