Chapter 8.3, Problem 4GP

To determine

An equation and solve it

Answer to Problem 4GP

The equation is $2x+54=132$

The solution of the equation is $x=39$

Explanation of Solution

Given:

Kendra pays $132 for shoes and clothes and the clothes cost $54 more than the shoes

Concept Used:

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.

In order to find an equation

Let x be the cost of the shoes

Since the clothes cost 54 more than the shoes as shown below,

  $2x+54=132$

Thus, the equation is $2x+54=132$

In order to solve the equation first subtract both sides by $54$ and then divide both sides by $2$ and then simplify as below

  $\begin{array}{l}2x+54=132\\ 2x+54-54=132-54\\ 2x=78\\ \frac{2x}{2}=\frac{78}{2}\\ x=39\end{array}$

Thus, the solution of the equation is $x=39$