Get personalized answers to your specific questions with IDNLearn.com. Ask your questions and receive prompt, detailed answers from our experienced and knowledgeable community members.

Recipe ingredients remain in a constant ratio no matter how many servings are prepared. Which of the following tables represents a possible ratio of ingredients [tex]$X$[/tex] and [tex]$Y$[/tex] for the given number of servings?

\begin{tabular}{|c|c|c|}
\hline
Servings & [tex]$X$[/tex] & [tex]$Y$[/tex] \\
\hline
1 & 1 & 2 \\
\hline
2 & 2 & 3 \\
\hline
3 & 3 & 4 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|c|}
\hline
Servings & [tex]$X$[/tex] & [tex]$Y$[/tex] \\
\hline
1 & 1 & 2 \\
\hline
2 & 2 & 4 \\
\hline
3 & 3 & 8 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|c|}
\hline
Servings & [tex]$X$[/tex] & [tex]$Y$[/tex] \\
\hline
1 & 1 & 2 \\
\hline
2 & 2 & 3 \\
\hline
3 & 3 & 5 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|c|}
\hline
Servings & [tex]$X$[/tex] & [tex]$Y$[/tex] \\
\hline
1 & 1 & 2 \\
\hline
2 & 2 & 4 \\
\hline
\end{tabular}


Sagot :

Sure, let's analyze each table step-by-step to determine whether the ratios of ingredient [tex]\( Y \)[/tex] to ingredient [tex]\( X \)[/tex] remain constant.

### Table 1:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Servings} & X & Y \\ \hline 1 & 1 & 2 \\ \hline 2 & 2 & 3 \\ \hline 3 & 3 & 4 \\ \hline \end{array} \][/tex]

First, we'll calculate the ratios [tex]\( \frac{Y}{X} \)[/tex]:
1. [tex]\( \frac{2}{1} = 2 \)[/tex]
2. [tex]\( \frac{3}{2} = 1.5 \)[/tex]
3. [tex]\( \frac{4}{3} \approx 1.33 \)[/tex]

The ratios are 2, 1.5, and approximately 1.33; these are not constant.

### Table 2:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Servings} & X & Y \\ \hline 1 & 1 & 2 \\ \hline 2 & 2 & 4 \\ \hline 3 & 3 & 8 \\ \hline \end{array} \][/tex]

Next, we'll calculate the ratios [tex]\( \frac{Y}{X} \)[/tex]:
1. [tex]\( \frac{2}{1} = 2 \)[/tex]
2. [tex]\( \frac{4}{2} = 2 \)[/tex]
3. [tex]\( \frac{8}{3} \approx 2.67 \)[/tex]

The ratios are 2, 2, and approximately 2.67; these are not constant.

### Table 3:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Servings} & X & Y \\ \hline 1 & 1 & 2 \\ \hline 2 & 2 & 3 \\ \hline 3 & 3 & 5 \\ \hline \end{array} \][/tex]

Next, we'll calculate the ratios [tex]\( \frac{Y}{X} \)[/tex]:
1. [tex]\( \frac{2}{1} = 2 \)[/tex]
2. [tex]\( \frac{3}{2} = 1.5 \)[/tex]
3. [tex]\( \frac{5}{3} \approx 1.67 \)[/tex]

The ratios are 2, 1.5, and approximately 1.67; these are not constant.

### Table 4:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Servings} & X & Y \\ \hline 1 & 1 & 2 \\ \hline 2 & 2 & 4 \\ \hline \end{array} \][/tex]

Finally, we'll calculate the ratios [tex]\( \frac{Y}{X} \)[/tex]:
1. [tex]\( \frac{2}{1} = 2 \)[/tex]
2. [tex]\( \frac{4}{2} = 2 \)[/tex]

The ratios are 2 and 2; these are constant.

Thus, the table where the ingredient ratios [tex]\( Y \)[/tex] to [tex]\( X \)[/tex] remain constant is Table 4. Therefore, the correct table index is 4.
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Thank you for choosing IDNLearn.com for your queries. We’re here to provide accurate answers, so visit us again soon.