trent invested money at 6% and $300 less at 8%. his total annual interest income is $116. how much did trent invest at 6%?

Question

if you could list the steps to help me understand it that would be great. thanks

Answer 1

Hey Silas,

This math problem involves a combination of basic algebra and investment portfolio knowledge.

So let's look at what this involves >

In this particular case, we are given 4 separate pieces of information (or 'givens'), which are stated below:
{1} Trent invested some amount of money, represented by variable "x", at the annual return rate of 6%.
{2} Trent invested some amount of money, represented by term "x - 300", at the annual return rate of 8%.
{3} Trent made two and only two investments over the course of the year.
{4} Trent's annual interest income from his investments was $116.

Okay! This layout gives us a better understanding of what we're dealing with.

Now let's use this layout to solve the problem at hand >

Our equation is as follows: (x)*(.06) + (x-300)*(.08) = 116 ... and here's the arithmetic reasoning for how we got there:

1. We know that {1} Trent invested some amount of money, represented by variable "x", at the annual return rate of 6%., so that goes on the left side of the equation, because that's a part of Trent's investment earnings for the year. We also know that {2} Trent invested some amount of money, represented by term "x - 300", at the annual return rate of 8%. That also goes on the left side of the equation as the second part of Trent's investment earnings for the year. Note that we found term "x - 300" by using the information given to us about how much Trent initially invested in each investment he made... 
2. Let's finish dealing with the left side of the equation. We know that {3} Trent made two and only two investments over the course of the year, so by using the information given to us, we can sort out the left side of the equation by multiplying principal¹ (represented by "x" and "x - 300") by annual return rate² (represented by ".06" and ".08") as converted to decimal form - for each of Trent's two investments. We also know that {4} Trent's annual interest income from his investments was $116, so that goes on the right side of the equation, because it's how much money Trent made off his investments for the year.

Solving the equation yields the following:
(x)*(.06) + (x-300)*(.08) = 116
.06x + .08x - 24 = 116

.14x - 24 = 116

.14x = 140

x = 1000

We can clearly see now that Trent invested $1000 at 6%, and additionally, we know that Trent must have invested $700 at 8% (but we're not worried about that). 

I hope you found this answer to be both helpful and thorough. Best of luck with your studies!

Answer 2

x = money invested at 6%

 

x-300 = money invested at 8%

 

Since Trent't total annual interest income is $116, this would be represent by the percentage of each amount invested.

 

.06x + .08(x-300) = 116

 

.06x + .08x -24 = 116

 

.14x - 24 = 116

 

.14x = 140

 

x = $1000

 

Trent invested $1000 at 6%