Question

the ratio of used books to new books in a bookstore is 2:9. check all statements that must be true based on the statement above. if none of the statements is true, check
one of the above\. there are 9 used books to every 2 new books in the bookstore. for every 9 used books in the bookstore, there are 2 new books. for every 2 new books in the bookstore, there are 9 used books. for every 2 used books in the bookstore, there are 9 new books. none of the above

Explanation:

The ratio of used books to new books is \(2:9\), which means for every 2 used books, there are 9 new books. Let's analyze each statement:

• "There are 9 used books to every 2 new books": This reverses the ratio (should be 2 used to 9 new), so false.
• "For every 9 used books, there are 2 new books": Incorrect ratio (ratio is 2 used : 9 new, not 9 used : 2 new), false.
• "For every 2 new books, there are 9 used books": Incorrect (ratio is used : new = 2:9, so new : used = 9:2, meaning 2 new would correspond to \( \frac{4}{9} \) used? No, better to think original ratio: 2 used → 9 new. So 2 new would be \( \frac{2\times2}{9} \) used? No, the ratio is used : new = 2:9, so if new is 2, used is \( \frac{2\times2}{9} \)? No, that's not right. Wait, ratio \( a:b \) means \( \frac{\text{used}}{\text{new}}=\frac{2}{9} \), so \( \text{used}=\frac{2}{9}\text{new} \). So if new is 2, used is \( \frac{4}{9} \), not 9. So this statement is false.
• "For every 2 used books, there are 9 new books": This matches the ratio \( 2:9 \) (used : new), so this is true.

Answer:

For every 2 used books in the bookstore, there are 9 new books.