Chapter 8.3, Problem 5GP

To determine

An equation and how many cars did they wash during the spring car wash

Answer to Problem 5GP

The equation is $2x-14=96$

They washed cars $41$

Explanation of Solution

Given:

The activities Club washed 14 fewer cars than during the summer car wash and they washed total 96 cars during both car washes

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 summer car wash then the equation for summer is

  $2x-14=96$

Thus, the equation is $2x-14=96$

In order to solve the equation $2x-14=96$ first add both sides by $14$ and then divide both sides by $2$ and then simplify as below

  $\begin{array}{l}2x-14=96\\ 2x-14+14=96+14\\ 2x=110\\ \frac{2x}{2}=\frac{110}{2}\\ x=55\end{array}$

Thus, the solution of the equation for summer is $x=55$

For the spring

  $\begin{array}{c}Spring=96-Summer\\ =96-55\\ =41\end{array}$

Thus, they washed cars $41$