To determine the system of linear equations that represent the scenario, we need to translate the given information into mathematical equations using the variables [tex]\( h \)[/tex] (cost per hour of horseback riding) and [tex]\( j \)[/tex] (cost per hour of jet ski rental).
### Information provided:
1. The first package costs \[tex]$192 and includes 3 hours of horseback riding and 2 hours of jet ski rental.
2. The second package costs \$[/tex]213 and includes 2 hours of horseback riding and 3 hours of jet ski rental.
### Translating the information into equations:
1. For the first package:
The total cost is composed of the cost for horseback riding and the cost for jet ski rental.
[tex]\[ 3h + 2j = 192 \][/tex]
2. For the second package:
Similarly, the total cost here is also composed of the cost for horseback riding and the cost for jet ski rental.
[tex]\[ 2h + 3j = 213 \][/tex]
### System of Equations:
Combining both equations, we get the system:
[tex]\[ \begin{cases}
3h + 2j = 192 \\
2h + 3j = 213
\end{cases} \][/tex]
Thus, the system of linear equations representing this scenario is:
[tex]\[
\boxed{
\begin{array}{c}
3h + 2j = 192 \\
2h + 3j = 213
\end{array}
}
\][/tex]
