Chapter 8, Problem 33CR

To determine

An equation and how many months it would take for the total cost of the two plans to be the same

Answer to Problem 33CR

The equation is $20+5m=30+3m$

The months are $m=5$ .

Explanation of Solution

Given:

An online DVD rental club has two membership plans as shown

  

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 month

Let m be the month

For plan A $20 is the membership fee and $5 is the cost per month

So, the equation is $20+5m$

For plan B $30 is the membership fee and $3 is the cost per month

So, the equation is $30+3m$

Equate the both expression $20+5m=30+3m$

Thus, the equation is $20+5m=30+3m$

Here to isolate x on left side, first subtract both sides by $3m$ and then subtract both sides by $20$ and then divide both sides by $2$ and then simplify further as shown below,

  $\begin{array}{c}20+5m=30+3m\\ 20+5m-3m=30+3m-3m\\ 20+2m=30\\ 20+2m-20=30-20\\ 2m=10\\ \frac{2m}{2}=\frac{10}{2}\\ m=5\end{array}$

Thus, the months are $m=5$ .