Algebra Word problem help?

Teresa 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 $25 and an additional 70 cents for every mile driven.

Company B charges an initial fee of $65 and an additional 20 cents for every mile driven.

For what mileages will Company A charge no more than Company B?

Write your answer as an inequality, using m for the number of miles driven.

Comments

  • 25 + .7M = 65 + .2M or .5M = 40 hence M is 80 miles. Tada.

  • Company A cost= A; Company B cost=B (cost in cents)

    A=70x+2500, where x is the number of miles driven

    B=20x+6500, "" ""

    Point of intersection: A=B

    70x+2500=20x+6500

    50x=4000

    x=80

    Sketch graph or check with values above and below and see which is higher cost

    e.g) x=40

    A=2800+2500

    B=800+6500 ===> B>A

    so above the intersection, A>B

    The x values (m values) where A>B are

    m>80

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