Mrs. Price is a librarian at Central Library. In examining a random sample of the library's book collection, she found the following. 762 books had no damage,
83 books had minor damage, and
41 books had major damage.

Based on this sample, how many of the 51,500 books in the collection should Mrs. Price expect to have no damage or minor damage?
Round your answer to the nearest whole number. Do not round any intermediate calculations.

Step-by-step explanation:

We can start by finding the total amount of books to base our answer off of. 762 + 83 + 41 = 886. The chance of getting books with no damage equals 762/886 = 86.01%

Based off of this information, we can find 86.01% of 51,500. We can set up a proportion to solve. 51,500/x = 86.01/100. If you solve, you will get x = 44295.15.

It does not make sense to have .15 of a book leftover, so we need to round it to the nearest whole number as the problem asks us to do.

44295.15 about equals 44295 when rounded.

Mrs. Price can expect about 44295 books to have no damage.

Now we need to find how many books could have minor damage. Using what we know from our sample, we can predict that the chance of getting books that have minor damage equals 83/886 = 9.37%

Based off of this information, we can find 9.37% of 51,500. Using the proportion method, we can find that the answer is 4425.55. Once again, we need to round this answer to the nearest whole number. 4425.55 about equals 4426.

Mrs. Price can expect about 4426 books to have minor damage.

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