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Elam is packing his room to move into a new house. A small box can hold 8 books without breaking, while a large box can hold 12 books without breaking. He has at most 160 books to pack and less than 30 boxes total. Let [tex]$s$[/tex] represent the number of small boxes and [tex]$l$[/tex] represent the number of large boxes. The inequalities [tex]$s \geq 0$[/tex] and [tex]$l \geq 0$[/tex] are part of the system that models this scenario.

Which inequalities complete the system?

A. [tex]s - l \textless 30[/tex]

B. [tex]8s - 12l \leq 160[/tex]

C. [tex]s + 1 \textless 30[/tex]

D. [tex]8s + 12l \leq 160[/tex]

E. [tex]s + l \textgreater 30[/tex]

F. [tex]8s + 12l \leq 160[/tex]

G. [tex]s + l \textless 30[/tex]

H. [tex]8s + 12l \geq 160[/tex]

Answer :

To solve the problem, we want to find all the constraints that model the scenario of Elam packing his books. Let's break down the information given:

1. Boxes and Books:
- A small box can hold 8 books.
- A large box can hold 12 books.
- Elam has at most 160 books to pack.

2. Boxes Limit:
- Elam can use less than 30 boxes in total.

Given these points, we can set up inequalities to properly model the situation:

- Books Constraint:
Since each small box holds 8 books and each large box holds 12 books, the total number of books Elam can pack is given by:
[tex]\[
8s + 12l \leq 160
\][/tex]
This inequality means that the total number of books in small (`s`) and large (`l`) boxes cannot exceed 160.

- Boxes Constraint:
The total number of boxes used should be less than 30. Therefore, the constraint for the number of boxes is:
[tex]\[
s + l < 30
\][/tex]
This means that the sum of small and large boxes must be less than 30.

Therefore, the system of inequalities that represent this scenario is:
- [tex]\(8s + 12l \leq 160\)[/tex]
- [tex]\(s + l < 30\)[/tex]

These inequalities ensure that Elam's books do not exceed the packing capacity of the boxes and that the number of boxes remains within the limit.

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Rewritten by : Barada