Chapter 8.5, Problem 24IP

To determine

An equation and find the cost of one CD

Answer to Problem 24IP

The equation is $48+3x=7x$

The one CD cost is $x=12$ .

Explanation of Solution

Given:

Gabriella bought some supplies for $48 and then bought 3 CDs. Min did not buy any school supplies but bought 7 CDs. All the CDs cost the same amount and they spent the same amount of money

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 cost of 1 CD, so her total cost is

  $48+3x$

Min only bought 7 CDs, so her cost is $7x$

Since they spent the same amount of money, equate the both expression

Thus, the equation for both is $48+3x=7x$ .

In order to solve the equation $48+3x=7x$ first subtract both sides by $3x$ and then divide both sides by $4$ and then simplify further as below:

  $\begin{array}{c}48+3x=7x\\ 48+3x-3x=7x-3x\\ 48=4x\\ \frac{48}{4}=\frac{4x}{4}\\ 12=x\\ \Rightarrow x=12\end{array}$

Thus, the one CD cost is $x=12$ .