Math Problem Statement

Write the system of 3 linear equations in 3 variables that is described by the following: A person invested $17,000 for one year, part at 10%, part at 12%, and the remainder at 15%. (These are annual interest rates, not compounded in any way.) The total annual income from these investments was $2110. The amount of money invested at 12% was $1000 less than the amount invested at 10% and 15% combined

Solution

To model this scenario as a system of three linear equations in three variables, let's define the following variables:

  • xx: Amount invested at 10% interest.
  • yy: Amount invested at 12% interest.
  • zz: Amount invested at 15% interest.

Now, we derive the equations based on the given information:

  1. Total amount invested:
    x+y+z=17000x + y + z = 17000

  2. Total annual income from investments:

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
System of Equations

Formulas

x + y + z = 17000
0.10x + 0.12y + 0.15z = 2110
y = (x + z) - 1000

Theorems

Methods for solving systems of linear equations

Suitable Grade Level

Grades 9-12

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