To tackle this problem, we'll translate the given conditions into a system of equations and then identify which option correctly represents this system.
1. Revenue from New and Used Books:
- The bookstore sells new books for [tex]$15 each.
- The bookstore sells used books for $[/tex]7 each.
- The total revenue last month was $234.
Given this information, we can set up the first equation to represent the total revenue:
[tex]\[ 15n + 7u = 234 \][/tex]
2. Relation between New and Used Books Sold:
- The store sold 2 more used books than new books.
This relationship can be written as:
[tex]\[ u = n + 2 \][/tex]
3. System of Equations:
Combining these two pieces of information, we get the system of equations:
[tex]\[ 15n + 7u = 234 \][/tex]
[tex]\[ u = n + 2 \][/tex]
4. Check the Options:
- Option A: [tex]\( 15n + 7u = 234 ; u = n - 2 \)[/tex]
- Option B: [tex]\( 7n + 15u = 234 ; u = n - 2 \)[/tex]
- Option C: [tex]\( 7n + 15u = 234 ; u = n + 2 \)[/tex]
- Option D: [tex]\( 15n + 7u = 234 ; u = n + 2 \)[/tex]
Looking at these options, the correct representation of the situation is as follows:
[tex]\[ 15n + 7u = 234 \][/tex]
[tex]\[ u = n + 2 \][/tex]
This matches option D.
Therefore, the system of equations that correctly represents this scenario is:
[tex]\[ \boxed{15n + 7u = 234 ; u = n + 2} \][/tex]
The correct answer is D.
