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,
[tex]\begin{gathered} t=a\times n \\ t=85\times12 \\ t=1020 \end{gathered}[/tex]The total score of 13 students is,
[tex]\begin{gathered} T=A\times N \\ T=82\times13 \\ T=1066 \end{gathered}[/tex]Now, Bob's score can be calculated as,
[tex]\begin{gathered} B=T-t \\ B=1066-1020 \\ B=46 \end{gathered}[/tex]Therefore, Bob's score on the test is 46.
