Chapter 8, Problem 9PT

To determine

The formula $S=2ab+2bc+2ac$ for the variable c .

Answer to Problem 9PT

  $c=\frac{S-2ab}{2a+2b}$

Explanation of Solution

Given information:

The formula for the surface area S of a box is $S=2ab+2bc+2ac$ .

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

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.

Calculation:

In order to solve for the variable c , first subtract both sides by 2ab and then divide both sides by 2a + 2b to simplify further as shown below:

  $\begin{array}{l}S=2ab+2bc+2ac\\ S-2ab=2ab-2ab+2bc+2ac\\ S-2ab=2bc+2ac\\ S-2ab=c\left(2a+2b\right)\\ \frac{S-2ab}{2a+2b}=\frac{c\left(2a+2b\right)}{2a+2b}\\ c=\frac{S-2ab}{2a+2b}\end{array}$

Thus, the formula for the variable is $c=\frac{S-2ab}{2a+2b}$ .