David expressed the ratio of the number of books that he owns to the number of DVDs that he owns as 27:11. Which statement could be true based upon this relationship?

Question

David has 11 books and 27 DVDs.
David has 11 DVDs and 27 books.
David has 11 DVDs and 27 items total.
David has 11 books and 27 items total

Answer 1

The ratio of the number of books to the number of DVDs that David owns is given as 27:11. This means for every 27 books, there are 11 DVDs.

Let's analyze the statements:

1. David has 11 books and 27 DVDs.

   • This is incorrect because it reverses the ratio. According to the ratio, David should have more books than DVDs.

2. David has 11 DVDs and 27 books.

   • This is correct because it matches the given ratio (27 books to 11 DVDs).

3. David has 11 DVDs and 27 items total.

   • This is incorrect. If he has 11 DVDs, to maintain the ratio of 27:11, he would need \(27 \times \frac{11}{11} = 27\) books, leading to a total of 38 items, not 27.

4. David has 11 books and 27 items total.

   • This is incorrect. If he had 11 books, to maintain the ratio, he would have \(11 \times \frac{27}{11} = 27\) DVDs, resulting in a total of 38 items, not 27.

Based on this analysis, the statement that could be true is:

David has 11 DVDs and 27 books.