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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 :

GinnyAnswer
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.
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