SOLUTION: A person ivested $6,700 for one year, part at 8%, part at 10%, and the remained at 12%. The total annual income from these investments was $716. The amount of money invested at 12%

Question 1140346: A person ivested $6,700 for one year, part at 8%, part at 10%, and the remained at 12%. The total annual income from these investments was $716. The amount of money invested at 12% was $300 more than the amount invested at 8% and 10% combined. Let x is the amount of money invested at 8%, y is the amount of money invest at 10%, and z is the amount of money invested at 12%.
a. Write the linear system of equations that models the conditions of the problem.
b. Write the augmented matrix for the system of linear equations

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The problem tells you the variables to use:
x = amount at 8%
y = amount at 10%
z = amount at 12%

(1) "A person invested $6,700..." --> x+y+z = 6700

(2) "The total annual income from these investments was $716." --> .08x+.10y+.12z = 716

(3) "The amount of money invested at 12% was $300 more than the amount invested at 8% and 10% combined." --> z = x+y+300

(a) The three equations are

x+y+z = 6700
.08x+.10y+.12z = 716
z = x+y+300

(b) For solving the system using matrices, the equations must be in the form Ax+By+Cz = D. Two of the three equations are already in that form; you need to do a bit of work on the third one.

Then the augmented matrix is the coefficients of the three equations....
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