Jacob wants to use an elevator to carry identical packages, each weighing 3 pounds, while he himself weighs 99 pounds. The elevator can carry a maximum of 300 pounds at a time.

Which inequality shows the maximum number of packages, \( n \), that Jacob can carry with himself in the elevator if he is the only passenger?

Question

Middle School

Answer :

FelisFelis FelisFelis · Answer 1 · 2024-04-23T13:39:43-04:00

Answer:

The required inequality that shows the maximum number of packages is [tex]n\leq 67[/tex].

Step-by-step explanation:

Consider the provided information.

Each package weighs 3 pounds and Jacob weighs 99 pounds.

let n is the maximum number of package that Jacob can carry with himself in the elevator.

Thus, the total weight of Jacob while having n packages on the elevator is:

[tex]3n+99[/tex]

The elevator can carry a maximum of 300 pounds at a time, therefore.

[tex]3n+99\leq 300[/tex]

Now, subtract 99 from both sides and divide the obtained inequality with 3.

[tex]3n+99-99\leq 300-99[/tex]

[tex]3n\leq 201[/tex]

[tex]\frac{3n}{3}\leq \frac{201}{3}[/tex]

[tex]n\leq 67[/tex]

Thus, the Jacob can carry maximum 67 packages.

Hence, the required inequality that shows the maximum number of packages is [tex]n\leq 67[/tex].