Let [tex] x_1,\ x_2,\ldots,\ x_8 [/tex] be the scores of the first 8 quizzes. We know that the average of these scores is 85, so we have
[tex] \dfrac{x_1+x_2+\ldots+x_8}{8} = 85 \iff x_1+x_2+\ldots+x_8 = 85 \cdot 8 = 680 [/tex]
The average of the first 9 scores is 81, and it is given by
[tex] \dfrac{x_1+x_2+\ldots+x_8+x_9}{9} = 81 [/tex]
But we know that the sum of the first 8 is 680:
[tex] \dfrac{680+x_9}{9} = 81 [/tex]
And we can solve for the nineth score: multiply both sides by 9:
[tex] 680+x_9 = 729 [/tex]
Subtract 680 from both sides:
[tex] x_9 = 729 - 680 = 49 [/tex]
