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Ivanna is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.

Company A charges 114 and allows unlimited mileage.
Company B has an initial fee of 65 and charges an additional 0.70 for every mile driven.
For what mileages will Company A charge less than Company B?
Use m for the number of miles driven, and solve your inequality for m

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  1. let the mileage be m

    65 + .7m < 114 + 0m
    .7m < 49
    m < 70

    so for m> 70 miles, company A is cheaper

    check:
    if m = 50
    company A charges $114
    company B charges 65 + .7(50) = 100

    if m = 71
    company A charges $114
    company B charges 65+.7(71) = $114.70 . which is more

    btw, if m = 70
    A charges $114
    B charges 65 + 70(.7) = 114 , the same

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  2. Melissa is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
    Company A charges an initial fee of $50 and an additional 80 cents for every mile driven.
    Company B charges an initial fee of 65$ and an additional 60
    cents for every mile driven.

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  3. Lena is choosing between two exercise routines.
    In Routine #1, she does only running, burning 10.5 calories per minute.
    In Routine #2, she burns 23 calories walking. She then runs at a rate that burns 4.75 calories per minute.
    For what amounts of time spent running will Routine #1 burn more calories than Routine #2?
    Use for the number of minutes spent running, and solve your inequality for .

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