Michelle and Michael checked some books out of the library. 20% of the books Michelle checked out were fiction books, and 40% of the books Michael checked out were fiction books. Your friend thinks that Michael checked out more fiction books than Michelle. Explain the error in your friend's thinking. Use an example to support your reasoning.

Given:

Michelle and Michael checked some books out of the library. 20% of the books Michelle checked out were fiction books, and 40% of the books Michael checked out were fiction books.

To Find:

The error in the assessment that Michael checked out more fiction books than Michelle.

Answer:

We can determine who has more fiction books only when we know how many books each person has checked out in total and not by simply looking at the proportion of fiction books (20% and 40%) at face value.

Step-by-step explanation:

40% of the books Michael has checked out is fiction and 20% of the books Michelle has checked out is fiction.

So at face value, it is easy to assume that since 40 is greater than 20, it must be that Michael has checked out more fiction books.

However, the key to understanding the error in the assumption is that it is not given in the question that Michelle and Michael have borrowed the same number of books!

We must note the fact that we don't know how many books Michael and Michelle have checked out. The information given in the question is not enough to deduce who has more fiction books.

Say for example Michael has checked out 10 books and Michelle has checked out 40 books.

Then the number of fiction books Michael has is

40% of 10 books i.e., 4 books since

The number of fiction books Michelle has is 20% of 40 which is

i.e., Michelle has checked out 8 fiction books. We can see in this case that Michelle has actually checked out more books than Michael has.

If it was given that both Michael and Michelle have borrowed the same number of books (maybe say, 10 books each), then 20% of Michelle's books are fiction which implies she has checked out

i.e., 2 fiction books.

Similarly, as 40% of the books Michael has checked out is fiction, he has checked out 4 fiction books.

In this case, Michael has checked out more fiction books than Michelle.

Thus we can determine who has more fiction books only when we know how many books each person has checked out.