Chapter 8.7, Problem 23IP

To determine

Write and solve an inequality to find how many video games he can play.

Answer to Problem 23IP

  $2+0.75x\le 10$ ; Montel can play at most 10 video games.

Explanation of Solution

Given:

Montel pays a $2 entrance fee and $0.75 every time he plays his favourite video game. If he has $10, write and solve an inequality to find how many video games he can play.

Concept Used:

Translate the sentence into an inequality.

Entrance fee is $2 and $0.75 every time he plays his favourite video game.

Let the number of time he plays his favourite video game is x.

The required inequality: $2+0.75x\le 10$

Calculation:

Let the number of time he plays his favourite video game is x.

The required inequality: $2+0.75x\le 10$

  $\begin{array}{l}2+0.75x\le 10\\ 2-2+0.75x\le 10-2\text{[}\text{Subtract}\text{from}\text{both}\text{sides}\text{]}\\ 0.75x\le 8\\ \frac{0.75x}{0.75}\le \frac{8}{0.75}\text{[}\text{Divide}\text{both}\text{sides}\text{by}0.75\text{]}\\ x\le 10.7\end{array}$

So, Montel can play at most 10 video games.

Thus, Montel can play at most 10 video games.