Uhave $20 to spend on taxi fare. the ride costs $5 plus $2.50 per mile. let m represent the number of miles ridden. write

Uhave $20 to spend on taxi fare. the ride costs $5 plus $2.50 per mile.
let m represent the number of miles ridden. write an inequality to determine how many miles you can ride for$20

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  1. In total you have $20.

    Base fare of taxi is $5.

    Per mile cost is $2.50.

    Your total cost is [tex]5+2.5x[/tex] where x is the number of miles. Since you're on a budget of maximum $20, the cost should be less than or equal to $20. We can write:

    [tex]5+2.5x\leq 20[/tex]

    To find how many miles we can write, let's solve the inequality:

    [tex]5+2.5x\leq20\\2.5x\leq20-5\\2.5x\leq15\\x\leq\frac{15}{2.5} \\x\leq6[/tex].

    This means 6 is the maximum number of miles you can ride with $20.

    ANSWER: Maximum 6 miles

  2. [tex]2.50d+5\leq 20[/tex]

    Step-by-step explanation:

    Let d represent distance in kilometers.

    We have been given that a taxi ride costs $2.50 per kilometer, so the cost of d kilometers would be [tex]2.50d[/tex] dollars.

    We are also told that ride costs a fixed charge of $5, so total cost of d kilometers would be [tex]2.50d+5[/tex] dollars.

    You have $20 to spend on taxi fare, so the total cost of riding d kilometers should be less than or equal to 20.

    We can represent this information in an inequality as:

    [tex]2.50d+5\leq 20[/tex]

    Therefore, our required inequality would be [tex]2.50d+5\leq 20[/tex].

  3. d = 6 km

    Step-by-step explanation:

    The total cost of a ride includes a fixed, up-front cost and a variable cost:

    C(x) = $5.00 + ($2.50/km)x, where x is the number of kilometers covered.

    Setting C(x) = $20, we get:

    $20 = $5 + ($2.50/km)x

    which needs to be solved for x:

    $15 = ($2.50/km)x

    Dividing both sides by ($2.50/km) yields

    6 km = d

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