The equation \(8(n+6)=104\) can represent a real-world problem involving a scenario where a group of people is sharing a total amount of something, such as money or materials, evenly.
Real-World Problem:
Imagine a scenario where a teacher has 104 pencils and she wants to distribute them equally among several students. However, before distributing, she plans to add 6 extra pencils to each student's share as a bonus. If the total number of students sharing the pencils is represented by \(n\), then the equation represents the situation where the teacher calculates the total amount of pencils including the bonus:
- The expression \(n + 6\) represents the amount of pencils each student receives (the \(n\) students each get 6 extra pencils).
- Multiplying this by 8 signifies that there are 8 students in total.
- The result, 104, represents the total number of pencils available.
To solve for \(n\), the teacher would be determining how many students (without extra pencils) are sharing the pencils after accounting for the bonus. This means she wants to find out how many students can fit into that structure and still keep the total distribution equal to 104 pencils.
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