Let's solve this step by step:

Step 1: Let's denote the number of students who failed Quiz 1 as F1 and the number of students who passed Quiz 1 as P1. According to the problem, the ratio of passes to failures in Quiz 1 is 3:1, so we can write this as P1/F1 = 3/1, or P1 = 3F1.

Step 2: Similarly, let's denote the number of students who failed Quiz 2 as F2 and the number of students who passed Quiz 2 as P2. The ratio of passes to failures in Quiz 2 is 4:1, so we can write this as P2/F2 = 4/1, or P2 = 4F2.

Step 3: The problem also tells us that the number of failures in Quiz 2 is one less than that in Quiz 1, so we can write this as F2 = F1 - 1.

Step 4: The total number of students in the class is the sum of the number of passes and failures in either Quiz 1 or Quiz 2 (since there were no absentees), so we can write this as Total = P1 + F1 = P2 + F2.

Step 5: Substituting P1 = 3F1 and P2 = 4F2 into the equation from Step 4 gives us Total = 3F1 + F1 = 4F2 + F2.

Step 6: Substituting F2 = F1 - 1 into the equation from Step 5 gives us Total = 4F1 - 4 + F1 - 1 = 4F1.

Step 7: Solving for F1 gives us F1 = 5.

Step 8: Substituting F1 = 5 into the equation P1 = 3F1 gives us P1 = 15.

Step 9: Therefore, the total number of students in the class is Total = P1 + F1 = 15 + 5 = 20.

Question

Let's solve this step by step:

Step 1: Let's denote the number of students who failed Quiz 1 as F1 and the number of students who passed Quiz 1 as P1. According to the problem, the ratio of passes to failures in Quiz 1 is 3:1, so we can write this as P1/F1 = 3/1, or P1 = 3F1.

Step 2: Similarly, let's denote the number of students who failed Quiz 2 as F2 and the number of students who passed Quiz 2 as P2. The ratio of passes to failures in Quiz 2 is 4:1, so we can write this as P2/F2 = 4/1, or P2 = 4F2.

Step 3: The problem also tells us that the number of failures in Quiz 2 is one less than that in Quiz 1, so we can write this as F2 = F1 - 1.

Step 4: The total number of students in the class is the sum of the number of passes and failures in either Quiz 1 or Quiz 2 (since there were no absentees), so we can write this as Total = P1 + F1 = P2 + F2.

Step 5: Substituting P1 = 3F1 and P2 = 4F2 into the equation from Step 4 gives us Total = 3F1 + F1 = 4F2 + F2.

Step 6: Substituting F2 = F1 - 1 into the equation from Step 5 gives us Total = 4F1 - 4 + F1 - 1 = 4F1.

Step 7: Solving for F1 gives us F1 = 5.

Step 8: Substituting F1 = 5 into the equation P1 = 3F1 gives us P1 = 15.

Step 9: Therefore, the total number of students in the class is Total = P1 + F1 = 15 + 5 = 20.

Knowee AI · Accepted Answer