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 as, sixteen girls received as. out of the total fifty - four bs, thirty girls received bs. twelve boys received a c out of the twenty - four total cs on the test. which two - way table represents this information?

Explanation:

Step1: Calculate boys' A - grade count

Total A's = 28, girls' A's = 16. So boys' A's = \(28 - 16=12\)

Step2: Calculate boys' B - grade count

Total B's = 54, girls' B's = 30. So boys' B's = \(54 - 30 = 24\)

Step3: Check boys' total

Given boys' total (who received A, B or C) = 48. Boys' A + boys' B+ boys' C: \(12 + 24+12=48\) (since boys' C = 12 as given)

Step4: Check girls' total

Total sophomores = 106, boys (A + B + C)=48. So girls' total = \(106 - 48 = 58\)

Step5: Check totals of A, B, C

A: \(12 + 16=28\), B: \(24+30 = 54\), C: \(12+12=24\), total \(28 + 54+24=106\)

Answer:

The second two - way table (where Boys' A = 12, Boys' B = 24, Boys' C = 12, Girls' A = 16, Girls' B = 30, Girls' C = 12, Total A = 28, Total B = 54, Total C = 24, Boys' Total = 48, Girls' Total = 58, Grand Total = 106)