official practice test 3 section 4 how to solve?

The question tells you that the store’s average after 10 ratings is 75. That means that the first 10 ratings have a sum of 750, because \text{average}=\dfrac{\text{sum}}{\text{number of values}}, \text{average}\times\text{number of values}=\text{sum}. In this case, 75\times 10=750.

You need the first 20 ratings to have an average of 85, which means you need the sum of the first 20 ratings to be 20\times 85=1700. So far so good?

Now, we know that the first 10 ratings added to 750, so we need the next 10 ratings to add to 1700-750=950.

Since we want to know the smallest possible value for the 11th rating, let’s assume that the 12th-20th ratings are the highest they can be, 100. In other words, let’s assume there are 9 perfect 100 ratings, and set the 11th rating equal to x.



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