creating a two - way table\nout of 106 total sophomores, there were forty - eight boys who received either…

creating a two - way table\nout 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?\na b c total\nboys 44 84 24 106\ngirls 28 54 12 58\ntotal 16 30 12 48\na b c total\nboys 12 24 12 48\ngirls 16 30 12 58\ntotal 28 54 24 106\na b c total\nboys 16 30 12 58\ngirls 12 24 12 48\ntotal 28 54 24 106
Answer
Explanation:
Step1: Calculate number of boys with A
Total A's are 28 and 16 girls received A's. So number of boys with A is $28 - 16=12$.
Step2: Calculate number of boys with B
Total B's are 54 and 30 girls received B's. So number of boys with B is $54 - 30 = 24$.
Step3: Check total number of boys
We know there are 48 boys who received A, B or C. And number of boys with A is 12, with B is 24 and with C is 12 ($12 + 24+12=48$).
Step4: Calculate number of girls with C
Total C's are 24 and 12 boys received C's. So number of girls with C is $24 - 12 = 12$.
Step5: Calculate total number of girls
Total sophomores are 106 and 48 are boys. So number of girls is $106 - 48=58$. And $16 + 30+12 = 58$ (number of girls with A, B and C respectively).
Step6: Check total columns
Total A's: $12 + 16=28$. Total B's: $24 + 30 = 54$. Total C's: $12+12 = 24$. Total students: $48 + 58=106$.
Answer:
The second two - way table (Boys: 12, 24, 12, 48; Girls: 16, 30, 12, 58; Total: 28, 54, 24, 106) represents the information.