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?
A. David has 11 books and 27 DVDs.
B. David has 11 DVDs and 27 books.
C. David has 11 DVDs and 27 items total.
D. David has 11 books and 27 items total.
Answer (2)
The ratio of books to DVDs is 27:11, meaning the number of books is 27 x and the number of DVDs is 11 x for some positive integer x .
Check each statement to see if it aligns with the given ratio.
Only the statement 'David has 11 DVDs and 27 books' holds true when x = 1 .
Therefore, the correct answer is 'David has 11 DVDs and 27 books'. $\boxed{David has 11 DVDs and 27 books.}
Explanation
Understanding the Ratio Let's analyze the given problem. David has books and DVDs, and the ratio of books to DVDs is 27:11. This means for some positive integer x , the number of books is 27 x and the number of DVDs is 11 x . We need to determine which of the given statements could be true based on this relationship.
Checking Each Statement Now, let's examine each statement:
David has 11 books and 27 DVDs. This would mean 27 x = 11 and 11 x = 27 . Solving for x in each equation gives x = 27 11 and x = 11 27 . Since x must be the same in both cases, this statement cannot be true.
David has 11 DVDs and 27 books. This would mean 27 x = 27 and 11 x = 11 . Solving for x in each equation gives x = 1 and x = 1 . Since x is the same in both cases, this statement could be true.
David has 11 DVDs and 27 items total. This would mean 11 x = 11 and 27 x + 11 x = 27 . This simplifies to 11 x = 11 and 38 x = 27 . Solving for x in each equation gives x = 1 and x = 38 27 . Since x must be the same in both cases, this statement cannot be true.
David has 11 books and 27 items total. This would mean 27 x = 11 and 27 x + 11 x = 27 . This simplifies to 27 x = 11 and 38 x = 27 . Solving for x in each equation gives x = 27 11 and x = 38 27 . Since x must be the same in both cases, this statement cannot be true.
Conclusion From the above analysis, only the second statement could be true.
Examples
Understanding ratios is crucial in everyday life. For instance, when baking, a recipe might call for a ratio of flour to sugar as 3:1. If you want to make a larger batch and use 6 cups of flour, you can use the ratio to determine that you'll need 2 cups of sugar to maintain the correct proportions. This ensures your baked goods turn out perfectly every time!
The ratio of David's books to DVDs is 27:11, meaning he could have 27 books if he has 11 DVDs. Evaluating the multiple-choice options, the statement that could be true is: David has 11 DVDs and 27 books. Therefore, the correct choice is option B.
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