Chapter 8.5, Problem 7GP

To determine

An equation and the number of DVDs so the cost for each will be same

Answer to Problem 7GP

The equation is $3.99x=1.99x+50$

The cost is $x=25$ .

Explanation of Solution

Given:

An internet movie rental company charges a yearly membership fee of $50 plus $1.99 per DVD rental and your neighborhood rental store has no membership fee and charges $3.99 per DVD rental.

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, the expression for the internet movie rental company at $1.99 plus a yearly fee of $50 as shown below,

  $1.99x+50$

The expression for the neighborhood rental fee and charges $3.99 for DVD is $3.99x$

In order to find the number of DVDs so the cost for each will be the same as below:

  $3.99x=1.99x+50$

In order to solve the equation $3.99x=1.99x+50$ first subtract both sides by $1.99x$ and then divide both sides by $2$ and then simplify further as below:

  $\begin{array}{c}3.99x=1.99x+50\\ 3.99x-1.99x=1.99x+50-1.99x\\ 2x=50\\ \frac{2x}{2}=\frac{50}{2}\\ x=25\end{array}$

Thus, the cost is $x=25$ .