It 1 of 2 While grocery shopping, Carmen spent \( \$ 13.66 \) and Andy spent \( \$ 61.63 \). Use rational numbers to write an expression that compares spending \( \$ 13.66 \) to spending \( \$ 61.63 \) interpreted as size of loss. Whicl riend spent less on groceries? Which expression correctly compares the number of dollars each friend spent? A. \( |-1366|>|-6163| \) B. \( 1366<6163 \) C. \( 1366>6163 \) D. \( |-1366|<|-6163| \)

To compare the spending of Carmen and Andy, we need to analyze the amounts they spent in terms of rational numbers. 1. **Identify the amounts spent:** - Carmen spent \( \$ 13.66 \) - Andy spent \( \$ 61.63 \) 2. **Convert the amounts to cents for easier comparison:** - Carmen's spending in cents: \( 13.66 \times 100 = 1366 \) - Andy's spending in cents: \( 61.63 \times 100 = 6163 \) 3. **Set up the comparison:** - We want to compare \( 1366 \) (Carmen's spending) and \( 6163 \) (Andy's spending). 4. **Determine which friend spent less:** - Since \( 1366 < 6163 \), Carmen spent less than Andy. 5. **Evaluate the expressions given:** - A. \( |-1366|>|-6163| \) → This is not correct because both absolute values are positive, and \( 1366 < 6163 \). - B. \( 1366<6163 \) → This is correct as it accurately reflects that Carmen spent less than Andy. - C. \( 1366>6163 \) → This is incorrect as it states the opposite of the comparison. - D. \( |-1366|<|-6163| \) → This is also correct since both absolute values are positive, but it is not the most straightforward comparison of spending. Thus, the correct expression that compares the number of dollars each friend spent is: **B. \( 1366<6163 \)**. This indicates that Carmen spent less than Andy.