Kaitlyn. Michael and Anthony drive together to visit their aunt and uncle. They decided to take turns driving. Kaitlyn drives for 24 miles. and Michael drives three times as far as Kaitlyn. Then Anthony drives twice as far as Kaitlyn and Michael combined. How far did Anthony drive? Estimate: Number models with unknown: Answer: Is your answer reasonable? Explain.

Let's break down the problem step by step. ### Known Conditions: 1. Kaitlyn drives for \( K = 24 \) miles. 2. Michael drives three times as far as Kaitlyn: \( M = 3K \). 3. Anthony drives twice as far as Kaitlyn and Michael combined: \( A = 2(K + M) \). ### Step 1: Calculate Michael's Distance Since Michael drives three times as far as Kaitlyn: \[ M = 3K = 3 \times 24 \] ### Step 2: Calculate Anthony's Distance First, we need to find the total distance driven by Kaitlyn and Michael combined: \[ K + M = 24 + M \] Now substituting \( M \): \[ K + M = 24 + 3 \times 24 = 24 + 72 = 96 \] Now, we can find Anthony's distance: \[ A = 2(K + M) = 2 \times 96 \] ### Step 3: Calculate the Final Answer Now, let's calculate \( A \): \[ A = 2 \times 96 = 192 \] ### Summary of Calculations - Kaitlyn drives \( K = 24 \) miles. - Michael drives \( M = 72 \) miles. - Anthony drives \( A = 192 \) miles. ### Answer - **Estimate:** Anthony drives approximately 192 miles. - **Number models with unknown:** - \( K = 24 \) - \( M = 3K \) - \( A = 2(K + M) \) - **Final Answer:** Anthony drove 192 miles. ### Reasonableness of the Answer The answer seems reasonable because: - Kaitlyn's distance is a manageable number (24 miles). - Michael's distance, being three times that of Kaitlyn, is also reasonable (72 miles). - Anthony's distance, being twice the combined distance of Kaitlyn and Michael, results in a larger number (192 miles), which is consistent with the driving distances involved. Thus, the calculations and the final answer are logical and consistent with the problem's conditions.