Algebra word problem

Question

sheryl won 60,000 on a slot machine in Las Vegas. She invested part of her money at 2% simple rate and the rest at 3%. In one year she earned a total of 1600 in interest. how much was invested at each rate?

Answer 1

First, set up an equation for the amount of interest earned: .02x+.03y=1,600

                                                                                     

Second, set up an equation for your total amount invested:      x+     y=60,000

 

(x=amount invested @ 2%, y=amount invested at @ 3%)

 

Third, set up a matrix to represent you equations [.02  .03][x]=[1,600]

                                                                                           [  1     1 ][y]  [60,000]

 

solve the matrix using the equation the inverse of your first matrix times your answer matrixand your answer is 

40,000 invested at 3% and 20,000 invested at 2%

 

 

*If you do not understand how to find the inverse of the matrix this link will help.

http://www.coolmath.com/algebra/24-matrices/07-solving-systems-using-matrices-03

*If you do not know how to multiply matrices this video will help.

https://www.khanacademy.org/math/precalculus/precalc-matrices/matrix_multiplication/v/multiplying-a-matrix-by-a-matrix

 

 

 *Or you could just plug it into your calculator if you can use one