Answered

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You are considering two activity packages while on vacation. One costs [tex]$\$[/tex]192[tex]$ and includes 3 hours of horseback riding on the beach and 2 hours of jet ski rental. The second costs $[/tex]\[tex]$213$[/tex] and includes 2 hours of horseback riding on the beach and 3 hours of jet ski rental.

Select the system of linear equations that represent this scenario. Let [tex]$h$[/tex] = cost of one hour of horseback riding and let [tex]$j$[/tex] = cost of renting a jet ski for one hour.

A.
[tex]\[
\begin{array}{l}
3h + 2j = 192 \\
2h + 3j = 213
\end{array}
\][/tex]

B.
[tex]\[
\begin{array}{l}
3h + 3j = 192 \\
2h + 2j = 213
\end{array}
\][/tex]

C.
[tex]\[
\begin{array}{l}
3h + 2j = 213 \\
2h + 3j = 192
\end{array}
\][/tex]

D.
[tex]\[
\begin{array}{l}
3h + 3j = 213 \\
2h + 2j = 192
\end{array}
\][/tex]

Sagot :

GinnyAnswer
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]
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