Question

Twelve students took a test and their average score was 85. However, Bob was sick that day. after Bob took the test, the average score dropped to 82. what was bob's score on the test?

Answer 1

To find out Bob's score on the test, we calculate the total score of all the students with and without Bob. Bob's score is found by subtracting the total score without Bob from the total score with Bob. Bob's score on the test is 46.

Step-by-step explanation:

To find out Bob's score on the test, we need to calculate the total score of all the students without Bob and the total score of all the students including Bob. Then, we can find Bob's score by subtracting the total score without Bob from the total score with Bob. Let's assume Bob's score is x.

Given that the average score of all the students without Bob is 85, and there were 12 students, we can calculate the total score without Bob as 85 x 12 = 1020.

After Bob took the test, the average score dropped to 82. So, the total score with Bob is 82 x 13 = 1066. We can now find Bob's score by subtracting the total score without Bob from the total score with Bob: x = 1066 - 1020 = 46.

Answer 2

Given:

Total number of students, n=12.

The average score of 12 students, a=85.

After Bob took the test, the number of students attended the test, N=13.

The new average score, A=82.

The total score of 12 students is the product of their average score and the number of students.

Hence, the total score of 12 students is,

`\begin{gathered} t=a* n \\ t=85*12 \\ t=1020 \end{gathered}`

The total score of 13 students is,

`\begin{gathered} T=A* N \\ T=82*13 \\ T=1066 \end{gathered}`

Now, Bob's score can be calculated as,

`\begin{gathered} B=T-t \\ B=1066-1020 \\ B=46 \end{gathered}`

Therefore, Bob's score on the test is 46.