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A truck rental company rents a moving truck for one day by charging \( \$ 22 \) plus \( \$ 0.09 \) per mile. Write a linear equation that relates the cost \( C \), in dollars, of renting the truck to the number \( x \) of miles driven. What is the cost of renting the truck if the truck is driven 199 miles? 333 miles? Type the linear equation that relates the cost \( C \), in dollars, of renting the truck to the number of \( x \) miles driven. \( C=\square \) (Use integers or decimals for any numbers in the expression. Do not include the \( \$ \) symbol in your answer.)

Ask by Macdonald Deleon. in the United States
Feb 04,2025

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The linear equation is \( C = 0.09x + 22 \). For 199 miles, the cost is \$39.91. For 333 miles, the cost is \$51.97.

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The Deep Dive

To find the linear equation that relates the cost \( C \) to the number of miles \( x \) driven, we can start with the base fee of the rental plus the mileage charge. The equation is: \[ C = 22 + 0.09x \] Now, let's find the cost for driving 199 miles and 333 miles: 1. For 199 miles: \[ C = 22 + 0.09(199) = 22 + 17.91 = 39.91 \] 2. For 333 miles: \[ C = 22 + 0.09(333) = 22 + 29.97 = 51.97 \] So, the costs are: - Driving 199 miles: \( C = 39.91 \) - Driving 333 miles: \( C = 51.97 \)

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