Chapter 3.4, Problem 23PPS

To determine

To calculate: The amount in each account A, B, and C.

Answer to Problem 23PPS

K invested 55000 dollars for account A,

20000 dollars for account B and 25000 dollars for account C.

Explanation of Solution

Given information :

Amount Invested by K = $100000

K invested $30,000 more in account A than account C and is expected to earn $ 6300 in interest

Calculation :

Consider a to be the amount invested in A, b to be amount invested B and c to the amount invested by C.

The system of equation representing the situation is written as follows:

  $\begin{array}{cc}a+b+c& =100000\\ a& =c+30000\end{array}$

Substitute $a=c+30000$ in equation one;

  $\begin{array}{cc}c+30000+b+c& =100000\\ 2c+b& =70000\end{array}$

The total interest amount is 6300, then;

  $0.04a+0.08b+0.1c=6300$

Substitute $a=c+30000$ in the above equation;

  $\begin{array}{cc}0.04(c+30000)+0.08b+0.1c& =6300\\ 0.14c+1200+0.08b& =6300\\ 0.14c+0.08b& =5100\end{array}$

Solve the equations as follows:

  $\begin{array}{r}\hfill \times (-0.8)\Rightarrow -0.16c-0.08b=-5600\\ \hfill 0.14c+0.08b=5100\\ \hfill -0.2c=-500\\ \hfill c=25000\end{array}$

Substitute $c=25000$ in equation two as follows:

  $\begin{array}{l}a=25000+30000\\ =55000\end{array}$

Substitute $c=25000$ in equation as follows:

  $\begin{array}{cc}2c+b& =70000\\ 2(25000)+b& =70000\\ 50000+b& =70000\end{array}$

Therefore,

  $\begin{array}{cc}b& =70000-50000\\ & =20000\end{array}$

The solution set is $\left(55000,20000,25000\right).$

Hence, the K invested 55000 dollars for account A, 20000 dollars for account B and 25000 dollars for account C.