To solve this problem, let's break it down step by step.
1. We are given that Carolyn is using a table to find 360% of 15.
2. The table provided includes the percentage values and their corresponding values for [tex]\( X \)[/tex] and [tex]\( Y \)[/tex].
3. Our goal is to determine the values of [tex]\( X \)[/tex] and [tex]\( Y \)[/tex] that fit the given percentages.
Looking at the table header:
- For [tex]\( 100\% \)[/tex], the value is [tex]\( X \)[/tex].
- For [tex]\( 20\% \)[/tex], the value is [tex]\( Y \)[/tex].
From the resulting answer provided:
- [tex]\( X \)[/tex] for 100% is found to be 15.
- [tex]\( Y \)[/tex] for 20% is found to be 3.
Now, let's match these values to the given options:
- [tex]\( X = 2.5 ; Y = 2.5 \)[/tex]
- [tex]\( X = 5 ; Y = 0.75 \)[/tex]
- [tex]\( X = 15 ; Y = 3 \)[/tex]
- [tex]\( X = 15 ; Y = 5 \)[/tex]
Since [tex]\( X = 15 \)[/tex] and [tex]\( Y = 3\)[/tex] are the correct calculated values:
The correct option is:
[tex]\( X = 15 ; Y = 3 \)[/tex].