Chapter 7.1, Problem 87E

To determine

To determine the system of equations under the given information and sketch the graph of the system of equations.

Answer to Problem 87E

Thesystem of linear equations is:

  $\text{Total}\text{amount}\text{invested:}x+y=20,000$

  $\text{Yearly interest:}5.5\%x+7.5\%y=1300$

Amount more than $20,000 must be invested in fund I to get the interest of $ 1300.

Explanation of Solution

Given information: The given information is:

Let $x\text{and}y$ be the amounts invested in two funds.

In fund I, rate of interest is 5.5 % and fund II, rate of interest is 7.5 % as simple interest.

The interest earned by investing $ 20,000 in two funds is $1300

Calculation:

(a) According to the information, the system of equations is:

  $\text{Total}\text{amount}\text{invested:}x+y=20,000$

  $\text{Yearly interest:}5.5\%x+7.5\%y=1300$

(b)  Using graphing utility to sketch the system of equations:

  $x+y=20,000$

  $55x+75y=1300000$

The graph is given as:

  

(c) In order to earn the interest of $ 1300 annually by invested some amount in fund I, the equations is:

  $5.5\%x=1300$

  $\Rightarrow x=23636.36\approx 23636$

Hence, to get interest of $ 1300, $ 23,636 must be invested in fund I.