Chapter 8.5, Problem 25IP

To determine

How many text messages is the cost of the plans the same

Answer to Problem 25IP

The text message is $x=100$ .

Explanation of Solution

Given:

One cell phone company charges $19.95 a month plus $0.21 per text message, and a second company charges $24.95 per month plus $0.16 per text message

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 find the given equation, let x be the number of text message. The first company charges $19.95 a month plus the cost of sending x text messages, so the cost is

  $19.95+0.21x$

The second company charges $24.95 a month plus the cost of x text messages, so the cost is $24.95+0.16x$

Since the cost is the same, so equate the both expression

Thus, the equation for both is $19.95+0.21x=24.95+0.16x$ .

In order to solve the equation $19.95+0.21x=24.95+0.16x$ first subtract both sides by $0.16x$ and then subtract both sides by $19.95$ and then divide both sides by $0.05x$ and then simplify further as below:

  $\begin{array}{c}19.95+0.21x=24.95+0.16x\\ 19.95+0.21x-0.16x=24.95+0.16x-0.16x\\ 19.95+0.05x=24.95\\ 19.95+0.05x-19.95=24.95-19.95\\ 0.05x=5\\ \frac{0.05x}{0.05}=\frac{5}{0.05}\\ x=100\end{array}$

Thus, the text message is $x=100$ .