Question

question 2 of 5
the ratio of used books to new books in a bookstore is 7:4.
check all statements that must be true based on the statement above.
if none of the statements is true, check
one of the above\.

• for every 4 used books in the bookstore, there are 7 new books.
• there are exactly 7 used books and exactly 4 new books in the bookstore.
• for every 7 new books in the bookstore, there are 4 used books.
• for every 7 used books in the bookstore, there are 4 new books.
• none of the above

Explanation:

Step1: Analyze the ratio

The ratio of used books to new books is \(7:4\), which means for every 7 used books, there are 4 new books.

Step2: Evaluate each statement

• "For every 4 used books in the bookstore, there are 7 new books." → Incorrect. The ratio is used to new as \(7:4\), not \(4:7\).
• "There are exactly 7 used books and exactly 4 new books in the bookstore." → Incorrect. The ratio \(7:4\) is a proportion, not the exact count. There could be \(14\) used and \(8\) new, etc., as long as the ratio is maintained.
• "For every 7 new books in the bookstore, there are 4 used books." → Incorrect. The ratio is used to new, so it's 7 used to 4 new, not 7 new to 4 used.
• "For every 7 used books in the bookstore, there are 4 new books." → Correct. This matches the given ratio \(7:4\) (used : new).
• "None of the above" → Incorrect since the fourth statement is true.

Answer:

The statement "For every 7 used books in the bookstore, there are 4 new books." is true. So we check that option.