\( 1 \leftarrow \quad \begin{array}{l}\text { A truck can be rented from Company A for } \$ 110 \text { a day plus } \$ 0.80 \text { per mile. Company B charges } \$ 40 \text { a day plus } \$ 0.90 \text { per mile to rent the same truck. How many miles must be driven } \\ \text { in a day to make the rental cost for Company A a better deal than Company B's? }\end{array} \)

To determine how many miles must be driven in a day for the rental cost from Company A to be a better deal than that from Company B, we can set up an inequality based on the costs from both companies. Let \( x \) be the number of miles driven in a day. The cost from Company A can be expressed as: \[ \text{Cost}_A = 110 + 0.80x \] The cost from Company B can be expressed as: \[ \text{Cost}_B = 40 + 0.90x \] We want to find the value of \( x \) for which the cost from Company A is less than the cost from Company B: \[ 110 + 0.80x < 40 + 0.90x \] Now, we will solve this inequality step by step. 1. Subtract \( 0.80x \) from both sides: \[ 110 < 40 + 0.10x \] 2. Subtract 40 from both sides: \[ 70 < 0.10x \] 3. Divide both sides by 0.10: \[ 700 < x \] This means: \[ x > 700 \] Thus, the number of miles that must be driven in a day for the rental cost from Company A to be a better deal than Company B's is more than 700 miles. In conclusion, the answer is: \[ \text{More than } 700 \text{ miles} \]