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Out of 106 total sophomores, there were forty-eight boys who received either an [tex]$A$[/tex], [tex]$B$[/tex], or [tex]$C$[/tex] on their first math test. Out of the twenty-eight total A's, sixteen girls received A's. Out of the total fifty-four B's, thirty girls received B's. Twelve boys received a C out of the twenty-four total C's on the test. Which two-way table represents this information?

\begin{tabular}{|c|c|c|c|c|}
\cline { 2 - 5 } \multicolumn{1}{c|}{} & A & B & C & Total \\
\hline Boys & 44 & 84 & 24 & 106 \\
\hline Girls & 28 & 54 & 12 & 58 \\
\hline Total & 16 & 30 & 12 & 48 \\
\hline
\end{tabular}

\begin{tabular}{|l|c|c|c|c|}
\cline { 2 - 5 } \multicolumn{1}{c|}{} & A & B & C & Total \\
\hline Boys & 12 & 24 & 12 & 48 \\
\hline Girls & 16 & 30 & 12 & 58 \\
\hline Total & 28 & 54 & 24 & 106 \\
\hline
\end{tabular}

\begin{tabular}{|c|c|c|c|c|}
\cline { 2 - 5 } \multicolumn{1}{c|}{} & A & B & C & Total \\
\hline Boys & 16 & 30 & 12 & 58 \\
\hline Girls & 12 & 24 & 12 & 48 \\
\hline Total & 28 & 54 & 24 & 106 \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To organize the given information into a proper two-way table, we need to summarize the counts of boys and girls who received grades A, B, or C. Let's go through the details step-by-step:

1. Total Sophomores: There are 106 total sophomores.

2. Total Boys with Grades:
- Boys who received grades: 48.

3. Details of A's:
- Total A's: 28.
- Girls who received A's: 16.
- Boys who received A's: [tex]\( 28 - 16 = 12 \)[/tex].

4. Details of B's:
- Total B's: 54.
- Girls who received B's: 30.
- Boys who received B's: [tex]\( 54 - 30 = 24 \)[/tex].

5. Details of C's:
- Total C's: 24.
- Boys who received C's: 12.
- Girls who received C's: [tex]\( 24 - 12 = 12 \)[/tex].

6. Total Boys and Girls:
- Total Boys (with grades A, B, or C): [tex]\( 12 + 24 + 12 = 48 \)[/tex].
- Total Girls: [tex]\( 106 - 48 = 58 \)[/tex].

Now we can construct the table using these numbers:

[tex]\[ \begin{tabular}{|l|c|c|c|c|} \cline{2-5} \multicolumn{1}{c|}{} & A & B & C & Total \\ \hline Boys & 12 & 24 & 12 & 48 \\ \hline Girls & 16 & 30 & 12 & 58 \\ \hline Total & 28 & 54 & 24 & 106 \\ \hline \end{tabular} \][/tex]

This result matches the second table provided in the options:

[tex]\[ \begin{tabular}{|l|c|c|c|c|} \cline { 2 - 5 } \multicolumn{1}{c|}{} & A & B & C & Total \\ \hline Boys & 12 & 24 & 12 & 48 \\ \hline Girls & 16 & 30 & 12 & 58 \\ \hline Total & 28 & 54 & 24 & 106 \\ \hline \end{tabular} \][/tex]

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