To determine which table could represent box number 5 based on the given ribbon proportions, we need to compare the ratios of pink to yellow ribbons in each table. Let's break it down step-by-step:
1. Identify the given ratios:
- The proportion of pink to yellow ribbons in Sandy's first four boxes can be represented by the ratio [tex]\(\frac{24}{30}\)[/tex].
2. Convert the given ratio to its simplest form for comparison:
[tex]\[
\frac{24}{30} = \frac{4}{5} = 0.8
\][/tex]
3. Calculate the ratio of pink to yellow ribbons in each given table option:
- Option 1:
[tex]\[
\frac{24}{30} = 0.8
\][/tex]
- Option 2:
[tex]\[
\frac{40}{60} = \frac{2}{3} \approx 0.6667
\][/tex]
- Option 3:
[tex]\[
\frac{8}{10} = 0.8
\][/tex]
- Option 4:
[tex]\[
\frac{3}{45} = \frac{1}{15} \approx 0.0667
\][/tex]
4. Compare each calculated ratio with the standard ratio of 0.8:
- Option 1: Ratio is 0.8, which matches the standard ratio.
- Option 2: Ratio is approximately 0.6667, which does not match the standard ratio.
- Option 3: Ratio is 0.8, which matches the standard ratio.
- Option 4: Ratio is approximately 0.0667, which does not match the standard ratio.
Therefore, the tables that could represent box number 5, having the same proportion of pink to yellow ribbons as in Sandy's first four boxes, are:
- Table in Option 1:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
\text{Box Number} & \text{Pink Ribbons} & \text{Yellow Ribbons} \\
\hline
5 & 24 & 30 \\
\hline
\end{tabular}
\][/tex]
- Table in Option 3:
[tex]\[
\begin{tabular}{|c|c|c|}
\hline
\text{Box Number} & \text{Pink Ribbons} & \text{Yellow Ribbons} \\
\hline
5 & 8 & 10 \\
\hline
\end{tabular}
\][/tex]
These two tables correctly represent box number 5 with the same pink to yellow ribbon proportion as in Sandy's first four boxes.
