Chapter 8.2, Problem 75STP

To determine

The number if text messages t she made in a month

Answer to Problem 75STP

The solution of the given equation is $t=111$

Option G is correct

Explanation of Solution

Given:

Ms. Fraser total monthly cell phone bill b can be found using the equation $b=45.60+0.10t$ and the total charge was $b=56.70$

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 $b=45.60+0.10t$ for the variable, isolate the variable term t on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate t on right side, first subtract both sides by $45.60$ and then divide both sides by $0.10$ and then simplify further as shown below,

  $\begin{array}{c}b=45.60+0.10t\\ 56.70=45.60+0.10t\\ 56.70-45.60=45.60+0.10t-45.60\\ 11.1=0.10t\\ \frac{11.1}{0.10}=\frac{0.10t}{0.10}\\ 111=t\\ \Rightarrow t=111\end{array}$

Thus, the solution of the given equation is $t=111$

Option G is correct