college algebra

Question

Walt made an extra $10,000 last year from a part-time job. He invested part of the money at 2% and the rest at 3.75%. He made a total of $270 in interest. How much was invested at 3.75%?

Answer 1

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 = 10000         because we know that he invested $10000 in total between the two assets

0.02x + 0.0375y = 270     because between the 2% return and 3.75% return he earned $270 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 = 4000, meaning that x = 10000 – 4000 = 6000

So he invested $4000 at the 3.75% rate and then the remaining $6000 at the 2% 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 :)

Answer 2

The way that this question by the author is confusing to a student.  However, it is not difficult.  This is simply a systems of equations problem.

 

First, let's piece together what exactly the question is asking us.

 

We are told that Walt has $10,000 to invest and he does so at 2 different percentage rates.  We are also told that he invests a certain amount at 2% and the remainder at 3.75%, earning $270 in interest  We will let x represent the amount invested at 2% and y represent the amount invested at 3.75%.

 

So, the amount total invested between x and y is $10,000 or (x + y = 10,000)

and the total amount earned in interest would be (0.02x + 0.0375y = 270)

 

Now we can go about solving the systems of equations; either by substitution, elimination, or graphically.  I prefer to solve using the substitution method so I will demonstrate that method in the following steps.

 

The purpose of substitution is to manipulate the equations such that you solve for a single variable and then SUBSTITUTE into the equation to solve for a numeric value by combining like terms.

 

We have         1X +         1Y = 10,000

                 0.02X + 0.0375Y =     270

 

Since the first equation expresses both variables with a coefficient of 1 I will solve for either variable.  In this case, I will solve for X:

 

 X + Y = 10,000

     - Y         -Y    

X        = 10,000 - Y

 

Now, we are saying that in the instance of X + Y = 10,000; X = 10,000 - Y

 

Now I will substitute this equation in the 2nd unsolved equation as follows:

 

0.02(10,000 - Y) + 0.0375Y = 270

 

Apply the Distributive Property

 

200 - 0.02Y + 0.0375Y = 270

 

Combine like terms

 

  200 + 0.0175Y = 270

 

Solve for Y

 

   200 + 0.0175Y = 270

 -200                    -200

0.0175Y = 70

0.0175    0.0175

 

Y = 4000

 

Substitute 4000 in for Y in original equation and solve for X

 

 

 

0.02X + 0.0375(4000) = 270

 

0.02X + 150 = 270

          - 150   - 150

0.02X          = 120

 

0.02X = 120

0.02      0.02

 

X = 6,000

 

Substitute both (x,y) into original equation

 

X + Y = 10,000

(6,000) + (4,000) = 10,000

 

True Statement