Alright, let's break down the problem step-by-step:
1. Define the variables:
- Let [tex]\( n \)[/tex] be the number of new books sold.
- Let [tex]\( u \)[/tex] be the number of used books sold.
2. Determine the book prices:
- Each new book is sold for \[tex]$12.
- Each used book is sold for \$[/tex]8.
3. Total revenue equation:
- The store earned a total revenue of \$112.
- Therefore, from the sale of new and used books, the total revenue equation can be formulated as follows:
[tex]\[
12n + 8u = 112
\][/tex]
4. Determine the relationship between the number of new and used books sold:
- The store sold 4 more used books than new books.
- Therefore, the relationship between [tex]\( n \)[/tex] and [tex]\( u \)[/tex] can be expressed as:
[tex]\[
u = n + 4
\][/tex]
5. Form the system of equations:
- Combining the total revenue equation and the relationship between the number of books sold, we get the system of equations:
[tex]\[
12n + 8u = 112
\][/tex]
[tex]\[
u = n + 4
\][/tex]
Hence, the correct system of equations that represents this scenario is:
[tex]\[
\boxed{12n + 8u = 112; \quad u = n + 4}
\][/tex]
Looking at the given options, the correct answer is:
C. [tex]\(12n + 8u = 112 ; u = n + 4\)[/tex]
