Math

A parcel delivery service charges $2.50 to deliver packages that weight 2 lb. The delivery packages weighing over 2 lb, but less than 3 1/2 lb, is $2.95. For packages weighing over 3 1/2 lb, but less than 5 lb, the fee is $3.40, and so on. Rosann uses the service to send a package and is charged $4.75. What is the range of the weight of her package?

Help, I don't know how much each intervals cost!

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  1. we have the piecewise cost function for weight w,

    c(w) =
    2.50 for w <= 2
    2.95 for 2 < x <= 3.5
    3.40 for 3.5 < x <= 5
    ...
    2.50 + .45⌈(w-2)/1.5⌉

    So, now we want w such that

    2.50 + .45⌈(w-2)/1.5⌉ = 4.75
    .45⌈(w-2)/1.5⌉ = 2.25
    ⌈(w-2)/1.5⌉ = 5
    4 < (w-2)/1.5 <= 5
    6 < w-2 <= 7.5
    8 < w <= 9.5

    check:
    continuing our piecewise table, we get
    3.40 for 3.5 < x <= 5
    3.85 for 5 < w <= 6.5
    4.30 for 6.5 < w <= 8
    4.75 for 8 < w <= 9.5

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