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Day and Night Kennel charges [tex]$\$[/tex]20[tex]$ per day plus a one-time food fee of $[/tex]\[tex]$15$[/tex] to board a pet. Bark Time Hotel charges [tex]$\$[/tex]30[tex]$ per day plus a one-time food fee of $[/tex]\[tex]$5$[/tex]. Which system of equations represents this real-world situation?

Let [tex]\( x \)[/tex] represent the number of days.

For Day and Night Kennel:
[tex]\[ y = 20x + 15 \][/tex]

For Bark Time Hotel:
[tex]\[ y = 30x + 5 \][/tex]

So, the system of equations is:
[tex]\[
\begin{cases}
y = 20x + 15 \\
y = 30x + 5
\end{cases}
\][/tex]



Answer :

GinnyAnswer
Let's analyze the given information step-by-step:

1. Day and Night Kennel:
- Charges [tex]\(\$20\)[/tex] per day to board a pet.
- Additionally, there is a one-time food fee of [tex]\(\$15\)[/tex].

Together, these charges can be represented as a tuple:
[tex]\[ (\text{Daily Charge}, \text{One-time Food Fee}) = (20, 15) \][/tex]

2. Bark Time Hotel:
- Charges [tex]\(\$30\)[/tex] per day to board a pet.
- Additionally, there is a one-time food fee of [tex]\(\$5\)[/tex].

Together, these charges can be represented as a tuple:
[tex]\[ (\text{Daily Charge}, \text{One-time Food Fee}) = (30, 5) \][/tex]

3. Summary:
- The system for Day and Night Kennel is represented as [tex]\((20, 15)\)[/tex].
- The system for Bark Time Hotel is represented as [tex]\((30, 5)\)[/tex].

Therefore, the tuple representation that matches this real-world situation is [tex]\(((20, 15), (30, 5))\)[/tex].

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