Chapter 7.1, Problem 87E

(a)

To determine

To evaluate: The system of equations for total amount and yearly interest.

Answer to Problem 87E

Therefore, the system of equations

  $\begin{array}{l}x+y=20000\\ 5.5x+7.5y=130000\end{array}$

Explanation of Solution

Given information: Total investment = $20000

Annual Interest	Rate 1	Rate 2
$1300	5.1%	7.5%

Formula used: For calculation of simple interest,

  $I=\frac{p\times r\times t}{100}$

where $p$ is principle amount, $r$ is rate of interest and $t$ is time period.

Calculation: The system of equations for amount invested at each rate,

  $\begin{array}{l}x+y=20000\\ 1300=\frac{x\times 5.5\times 1}{100}+\frac{y\times 7.5\times 1}{100}\\ \text{where }x\text{ and }y\text{ represents amount invested}\text{.}\end{array}$

Therefore, the system of equations

  $\begin{array}{l}x+y=20000\\ 5.5x+7.5y=130000\end{array}$

(b)

To determine

To graph: The system of equations for total amount and yearly interest.

Answer to Problem 87E

Therefore, the system of equations

  $\begin{array}{l}x+y=20000\\ 5.5x+7.5y=130000\end{array}$

  

Explanation of Solution

Given information: Total investment = $20000

Annual Interest	Rate 1	Rate 2
$1300	5.1%	7.5%

Formula used: For calculation of simple interest,

  $I=\frac{p\times r\times t}{100}$

where $p$ is principle amount, $r$ is rate of interest and $t$ is time period.

Calculation: The system of equations for amount invested at each rate,

  $\begin{array}{l}x+y=20000\\ 1300=\frac{x\times 5.5\times 1}{100}+\frac{y\times 7.5\times 1}{100}\\ \text{where }x\text{ and }y\text{ represents amount invested}\text{.}\end{array}$

Therefore, the system of equations can be represented as,

  

(c)

To determine

To evaluate: The system of equations for total amount and yearly interest.

Answer to Problem 87E

Therefore, the $10000 should be invested.

Explanation of Solution

Given information: Total investment = $20000

Annual Interest	Rate 1	Rate 2
$1300	5.1%	7.5%

Formula used: For calculation of simple interest,

  $I=\frac{p\times r\times t}{100}$

where $p$ is principle amount, $r$ is rate of interest and $t$ is time period.

Calculation: The system of equations for amount invested at each rate,

  $\begin{array}{l}x+y=20000\\ 1300=\frac{x\times 5.5\times 1}{100}+\frac{y\times 7.5\times 1}{100}\\ \text{where }x\text{ and }y\text{ represents amount invested}\text{.}\end{array}$

  $\text{At 5}\text{.5\%, }x=10000\text{ should be invested}$ because at this point for both rate of interest amount will be equal.