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The equation [tex]s=\frac{3}{4} f[/tex] represents the proportional relationship between the amount of sugar (s) and flour (f) in a recipe. Which table represents the equation of the proportional relationship?

A.
\begin{tabular}{|l|l|}
\hline
Sugar & Flour \\
\hline
1 & [tex]$\frac{6}{4}$[/tex] \\
\hline
2 & [tex]$\frac{3}{4}$[/tex] \\
\hline
\end{tabular}

B.
\begin{tabular}{|l|l|}
\hline
Sugar & Flour \\
\hline
[tex]$\frac{6}{4}$[/tex] & 1 \\
\hline
[tex]$\frac{3}{4}$[/tex] & 2 \\
\hline
\end{tabular}

C.
\begin{tabular}{|l|l|}
\hline
Sugar & Flour \\
\hline
[tex]$\frac{3}{4}$[/tex] & 1 \\
\hline
[tex]$\frac{6}{4}$[/tex] & 2 \\
\hline
\end{tabular}

D.
\begin{tabular}{|l|l|}
\hline
Sugar & Flour \\
\hline
1 & [tex]$\frac{3}{4}$[/tex] \\
\hline
2 & [tex]$\frac{6}{4}$[/tex] \\
\hline
\end{tabular}

Sagot :

GinnyAnsweridn
Let's analyze each of the given tables one by one to see which one represents the equation [tex]\( s = \frac{3}{4} f \)[/tex].

Table 1:
[tex]\[ \begin{array}{|c|c|} \hline \text{Sugar} & \text{Flour} \\ \hline 1 & \frac{6}{4} \\ \hline 2 & \frac{3}{4} \\ \hline \end{array} \][/tex]
For this table:
- For the first row: [tex]\(\frac{3}{4} \times \frac{6}{4} = \frac{18}{16} = 1.125 \neq 1\)[/tex]
- For the second row: [tex]\(\frac{3}{4} \times \frac{3}{4} = \frac{9}{16} \neq 2\)[/tex]

Both rows do not satisfy [tex]\( s = \frac{3}{4} f \)[/tex].

Table 2:
[tex]\[ \begin{array}{|c|c|} \hline \text{Sugar} & \text{Flour} \\ \hline \frac{6}{4} & 1 \\ \hline \frac{3}{4} & 2 \\ \hline \end{array} \][/tex]
For this table:
- For the first row: [tex]\(\frac{3}{4} \times 1 = \frac{3}{4} \neq \frac{6}{4}\)[/tex]
- For the second row: [tex]\(\frac{3}{4} \times 2 = \frac{6}{4} \neq \frac{3}{4}\)[/tex]

Both rows do not satisfy [tex]\( s = \frac{3}{4} f \)[/tex].

Table 3:
[tex]\[ \begin{array}{|c|c|} \hline \text{Sugar} & \text{Flour} \\ \hline \frac{3}{4} & 1 \\ \hline \frac{6}{4} & 2 \\ \hline \end{array} \][/tex]
For this table:
- For the first row: [tex]\(\frac{3}{4} \times 1 = \frac{3}{4} \rightarrow \text{True}\)[/tex]
- For the second row: [tex]\(\frac{3}{4} \times 2 = \frac{6}{4} \rightarrow \text{True}\)[/tex]

Both rows satisfy [tex]\( s = \frac{3}{4} f \)[/tex].

Table 4:
[tex]\[ \begin{array}{|c|c|} \hline \text{Sugar} & \text{Flour} \\ \hline 1 & \frac{3}{4} \\ \hline 2 & \frac{6}{4} \\ \hline \end{array} \][/tex]
For this table:
- For the first row: [tex]\(\frac{3}{4} \times \frac{3}{4} = \frac{9}{16} \neq 1\)[/tex]
- For the second row: [tex]\(\frac{3}{4} \times \frac{6}{4} = \frac{18}{16} \neq 2\)[/tex]

Both rows do not satisfy [tex]\( s = \frac{3}{4} f \)[/tex].

Based on the analysis above, the table that correctly represents the equation [tex]\( s = \frac{3}{4} f \)[/tex] is Table 3:

[tex]\[ \begin{array}{|c|c|} \hline \text{Sugar} & \text{Flour} \\ \hline \frac{3}{4} & 1 \\ \hline \frac{6}{4} & 2 \\ \hline \end{array} \][/tex]
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