1. **State the problem:** Michael has 1067.13 in his checking account. He plans to spend 510.71 on a television and the rest on speakers costing 46.00 each. We want to find the inequality that determines the maximum number of speakers $y$ he can buy without exceeding his total money. 2. **Set up the inequality:** The total amount spent on the television and speakers must be less than or equal to the total money available: $$510.71 + 46.00y \leq 1067.13$$ 3. **Explanation:** - $510.71$ is the fixed cost of the television. - $46.00y$ is the cost of $y$ speakers. - The sum must not exceed $1067.13$. 4. **Check the options:** - Option A: $510.71 \leq 46.00(y) + 1067.13$ (incorrect, reverses the inequality and adds money incorrectly) - Option B: $510.71 + 46.00 + y \leq 1067.13$ (incorrect, adds $46.00$ and $y$ incorrectly) - Option C: $1067.13 + 510.71 \geq 46.00 + y$ (incorrect, sums money and variables incorrectly) - Option D: $510.71 + 46.00(y) \leq 1067.13$ (correct) **Final answer:** Option D $$\boxed{510.71 + 46.00y \leq 1067.13}$$