If the first ten ratings received a score of 75 out of 100, we can denote this as 10(75), meaning that if the first 10 ratings were strictly 75 it would mean the same thing. Since we want to find the minimum for the 11th rating, we would want every other rating to have a score of 100, which would be denoted as 9(100). Let's denote the 11th rating as x, since that is what we are trying to find. To find the average, you add all the ratings and divide it by the number of ratings. So the equation thus follows:
[tex] \frac{10(75)+9(100)+x}{20} \geq 85
10(75)+9(100)+x= 1700
750+900+x=1700
1650+x=1700
x=50
[/tex]
The 11th rating could be 50 and the final average would still be 85
