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11. Make Sense and Persevere Talia has a daily budget of \( \$ 94 \) for a car rental. Write and solve an inequality to find the greatest distance Talia can drive each day while staying within her budget.

Ask by Boone Barnett. in the United States
Mar 18,2025

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To find the greatest distance Talia can drive each day while staying within her \$94 budget, set up the inequality: \[ \text{Cost per mile} \times \text{Distance} \leq 94 \] Solving for distance: \[ \text{Distance} \leq \frac{94}{\text{Cost per mile}} \] You need to know the cost per mile to determine the exact distance.

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The Deep Dive

Let's break this down! If Talia is budgeting \( \$ 94 \) daily for a car rental, we also need to know the cost per mile (or per distance unit) of the rental. Let's say it's \( x \) dollars per mile. The inequality would be \( 94 \geq x \cdot d \), where \( d \) represents the distance Talia can drive. Rearranging gives us \( d \leq \frac{94}{x} \). For example, if the rental costs \( \$ 0.50 \) per mile, then \( d \leq \frac{94}{0.50} = 188 \) miles. So, Talia can drive up to 188 miles a day while staying within her budget! Now that we've got the math cooked up, remember to consider any additional fees like insurance or fuel costs if applicable! Always check the total expenses to avoid that budget slip!

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