Expressions can be represented as equations or inequalities
- The inequality that represents the additional weight is: [tex]\mathbf{p \le 17}[/tex]
- The hiker can add additional 19.5 pounds
(a) Long hike
The hiker's weight is given as:
[tex]\mathbf{Weight =160}[/tex]
The hiker is embarking on a long hike, the recommended weight (x) of the backpack is calculated as:
[tex]\mathbf{x = 20\% \times 160}[/tex]
[tex]\mathbf{x = 32}[/tex]
The hiker's backpack weighs 15 lb.
So, the inequality that represents the additional weight is:
[tex]\mathbf{p + 15 \le 32}[/tex]
Subtract 15 from both sides
[tex]\mathbf{p \le 32 - 15}[/tex]
[tex]\mathbf{p \le 17}[/tex]
(b) Day hike
The hiker's weight is given as:
[tex]\mathbf{Weight =180}[/tex]
The hiker is embarking on a day hike (i.e. short hike), the recommended weight (x) is calculated as:
[tex]\mathbf{x = 15\% \times 180}[/tex]
[tex]\mathbf{x = 27}[/tex]
The hiker's backpack weighs 7.5 lb.
So, the additional weight the hiker can add is represented as:
[tex]\mathbf{p + 7.5 = 27}[/tex]
Subtract 7.5 from both sides
[tex]\mathbf{p = 27 - 7.5}[/tex]
[tex]\mathbf{p = 19.5}[/tex]
Hence, the hiker can add additional 19.5 pounds
Read more about equations and inequalities at:
https://brainly.com/question/11897796
