Question

out of 106 total sophomores, there were forty - eight boys who received either an a, b, or c 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? three two - way tables are shown with columns a, b, c, total and rows boys, girls, total. the first table: boys row has 44 (a), 84 (b), 24 (c), 106 (total); girls row has 28 (a), 54 (b), 12 (c), 58 (total); total row has 16 (a), 30 (b), 12 (c), 48 (total). the second table: boys row has 12 (a), 24 (b), 12 (c), 48 (total); girls row has 16 (a), 30 (b), 12 (c), 58 (total); total row has 28 (a), 54 (b), 24 (c), 106 (total). the third table: boys row has 16 (a), 30 (b), 12 (c), 58 (total); girls row has 12 (a), 24 (b), 12 (c), 48 (total); total row has 28 (a), 54 (b), 24 (c), 106 (total).

Explanation:

1. First, find the number of boys who received A's: Total A's are 28, and girls with A's are 16, so boys with A's = \(28 - 16 = 12\).
2. Next, find the number of boys who received B's: Total B's are 54, and girls with B's are 30, so boys with B's = \(54 - 30 = 24\).
3. We already know boys with C's are 12, and total boys are 48 (since \(12 + 24 + 12 = 48\)).
4. For girls: Total girls = \(106 - 48 = 58\). Girls with A's are 16, B's are 30, C's are \(24 - 12 = 12\) (since total C's are 24). Checking the totals: A's total \(12 + 16 = 28\), B's total \(24 + 30 = 54\), C's total \(12 + 12 = 24\), and overall total \(48 + 58 = 106\). This matches the second table.

Answer:

B. Boys: 12 (A), 24 (B), 12 (C), Total 48; Girls: 16 (A), 30 (B), 12 (C), Total 58; Total: 28 (A), 54 (B), 24 (C), Total 106