Chapter 8.5, Problem 39CCR

To determine

An equation and how long did their consultation last

Answer to Problem 39CCR

The equation is $22.50+17.50x=83.75$

The solution of the equation is $x=3.5$

Explanation of Solution

Given:

An accountant charges $22.50 plus $17.50 per hour for a consultation. The Chen family paid $83.75 for a tax consultation.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

In order to find an equation

Let x be per hour for a consultation

Since an accountant charges $22.50 plus $17.50 per hour for a consultation and family paid $83.75 for a tax as shown below,

  $22.50+17.50x=83.75$

Thus, the equation is $22.50+17.50x=83.75$

In order to solve the equation $22.50+17.50x=83.75$ first subtract both sides by $22.50$ and then divide both sides by $17.50$ and then simplify as below

  $\begin{array}{c}22.50+17.50x=83.75\\ 22.50+17.50x-22.50=83.75-22.50\\ 17.50x=61.25\\ \frac{17.50x}{17.50}=\frac{61.25}{17.50}\\ x=3.5\end{array}$

Thus, the solution of the equation is $x=3.5$