Chapter 8.2, Problem 52IP

To determine

The number of pages b in the first book

Answer to Problem 52IP

  $b=206$

Explanation of Solution

Given:

The second book in a fantasy series is 112 pages longer than the first book and the total number of pages in both books is 524 and the equation, $b+b+112=524$

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 the given equation $b+b+112=524$ for the variable, isolate the variable term b on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate b on left side, first add the like terms and then subtract both sides by $112$ and then divide both sides by $2$ and then simplify further as shown below,

  $\begin{array}{c}b+b+112=524\\ 2b+112=524\\ 2b+112-112=524-112\\ 2b=412\\ \frac{2b}{2}=\frac{412}{2}\\ b=206\end{array}$

Thus, the solution of the given equation is $b=206$ .