Chapter 9.2, Problem 26WE

To determine

To find: The solution of the given equations by using substitution method.

Answer to Problem 26WE

The solution of the given equations by using substitution method is $a=2000\text{and}b=3000$ .

Explanation of Solution

Given information:

The given equations are,

  $\begin{array}{l}a+b=5000\\ 0.08a=0.06b-20\end{array}$

The given equation can be written as,

  $\begin{array}{l}a+b=5000\\ a=5000-b\end{array}$

The another given equation is,

  $0.08a=0.06b-20$

Substitute $5000-b$ for $a$ .

  $\begin{array}{l}0.08\left(5000-b\right)=0.06b-20\\ 400-0.08b=0.06b-20\\ -0.08b-0.06b=-20-400\\ 0.14b=420\\ b=3000\end{array}$

The value of $a$ is calculated as,

  $\begin{array}{c}a=5000-b\\ =5000-3000\\ =2000\end{array}$

Thus, the solution of the given equations by using substitution method is $a=2000\text{and}b=3000$ .