Chapter 8.5, Problem 17IP

To determine

An equation and find how many songs Denzel would have to buy to spend the same amount at both websites

Answer to Problem 17IP

The equation is $5+0.5x=x$

The total songs are $x=10$ .

Explanation of Solution

Given:

Denzel is comparing websites for downloading music. One charges a $5 membership fee plus $0.50 per song. Another charges $1.00 per song but has no membership fee

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’s assume x be the number of songs Denzel downloads. The cost of downloading x songs as shown below:

  $5+0.5x$

The total cost of downloading from the second site is $1.0x$

Thus, the equation for both is $5+0.5x=x$ .

In order to solve the equation $5+0.5x=x$ first subtract both sides by $0.5x$ and then divide both sides by $0.5$ and then simplify further as below:

  $\begin{array}{c}5+0.5x=x\\ 5+0.5x-0.5x=x-0.5x\\ 5=0.5x\\ \frac{5}{0.5}=\frac{0.5x}{0.5}\\ 10=x\\ \Rightarrow x=10\end{array}$

Thus, the total songs are $x=10$ .