Question

David expresses the ratio of the of books that he owns to the number of books that he owns to the number of dvds that he owns as 27:11.What is the total number of items (books and DVDs) he owns if he has a total of 38 items?

A) 17 items

B) 22 items

C) 27 items

D) 33 items

E) 38 items

Answer 1

To find the total number of items that David owns, we set up a proportion based on the given ratio. Solving the proportion and the equation for the total number of items, we find that David owns 27 books and 11 DVDs.

Step-by-step explanation:

To find the total number of items that David owns, we need to determine the ratio between the number of books and the number of DVDs. The given ratio is 27:11. We can set up a proportion to solve for the number of books and DVDs. Let's say the number of books is x and the number of DVDs is y. We have the proportion 27/11 = x/y. Since we know that the total number of items is 38, we can set up another equation x + y = 38. Solving these two equations simultaneously, we find that x = 27/38 * 38 = 27 and y = 11/38 * 38 = 11. Therefore, David owns 27 books and 11 DVDs, totaling 38 items.