Chapter 2.2, Problem 25E

a.

To determine

To find : the inequality that represents the amount of weight can be added to the bag

Answer to Problem 25E

The inequality that represents how much weight can be added to the bag is $x\le 12$ where $x$ denotes the weight that can be added to the bag.

Explanation of Solution

Given information : A carry-on bag can weight no more than 50 pounds. A bag weighs 38 pounds

Formula used : Total weight of carry-on bag $\le 50$

Calculation :

Let $x$ denotes the weight that can be added to the bag.

Also, a bag weighs 38 pounds and a carry-on bag can weight no more than 50 pounds.

So,

  $\begin{array}{l}x+38\le 50\\ \Rightarrow x\le 50-38\\ \Rightarrow x\le 12\end{array}$

Therefore,

The inequality that represents how much weight can be added to the bag is $x\le 12$ where $x$ denotes the weight that can be added to the bag.

b.

To determine

To verify : If both a 9-pound laptop and a 5-pound pair of boots can be added to the bag without going over the weight limit.

Explanation of Solution

Given information : Both a 9-pound laptop and a 5-pound pair of boots are added to the bag.

Formula used : Check if $x=14$ satisfies the inequality obtained in part a.

Proof :

Total weight of a laptop and a pair of boots $=9+5=14$

Put $x=14$ satisfies the inequality obtained in part a.

  $14\le 12$ which is not true.

So, it’s not possible to add both a 9-pound laptop and a 5-pound pair of boots to the bag.