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Answer :
To solve this problem, we need to create a system of inequalities that represents the constraints given:
1. Constraints on the Number of Boxes:
- The problem states that Elam has less than 30 boxes in total. This includes both small and large boxes. This leads to the inequality:
[tex]\[
s + l < 30
\][/tex]
- Here, [tex]\( s \)[/tex] is the number of small boxes and [tex]\( l \)[/tex] is the number of large boxes.
2. Constraints on the Number of Books:
- Each small box can hold 8 books, and each large box can hold 12 books.
- Elam has at most 160 books to pack, which gives us the inequality:
[tex]\[
8s + 12l \leq 160
\][/tex]
By combining these conditions, we create a system of inequalities:
- [tex]\( s + l < 30 \)[/tex]
- [tex]\( 8s + 12l \leq 160 \)[/tex]
Additionally, we should note the non-negativity constraints already included:
- [tex]\( s \geq 0 \)[/tex] (Elam cannot use negative boxes)
- [tex]\( l \geq 0 \)[/tex] (Elam cannot use negative boxes)
These inequalities together model the constraints Elam must work within when packing his books.
1. Constraints on the Number of Boxes:
- The problem states that Elam has less than 30 boxes in total. This includes both small and large boxes. This leads to the inequality:
[tex]\[
s + l < 30
\][/tex]
- Here, [tex]\( s \)[/tex] is the number of small boxes and [tex]\( l \)[/tex] is the number of large boxes.
2. Constraints on the Number of Books:
- Each small box can hold 8 books, and each large box can hold 12 books.
- Elam has at most 160 books to pack, which gives us the inequality:
[tex]\[
8s + 12l \leq 160
\][/tex]
By combining these conditions, we create a system of inequalities:
- [tex]\( s + l < 30 \)[/tex]
- [tex]\( 8s + 12l \leq 160 \)[/tex]
Additionally, we should note the non-negativity constraints already included:
- [tex]\( s \geq 0 \)[/tex] (Elam cannot use negative boxes)
- [tex]\( l \geq 0 \)[/tex] (Elam cannot use negative boxes)
These inequalities together model the constraints Elam must work within when packing his books.
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