A carpet cleaner charges $75 to clean the first 180 sq ft of carpet. There is an additional charge

Discussion in 'Calculator Requests' started by math_celebrity, Jun 14, 2019.

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  1. math_celebrity

    math_celebrity Administrator Staff Member

    A carpet cleaner charges $75 to clean the first 180 sq ft of carpet. There is an additional charge of 25¢ per square foot for any footage that exceeds 180 sq ft and $1.30 per step for any carpeting on a staircase. A customers cleaning bill was $253.95. This included the cleaning of a staircase with 14 steps. In addition to the staircase, how many square feet of carpet did the customer have cleaned?

    Calculate the cost of the staircase cleaning.
    Staircase cost = $1.30 * steps
    Staircase cost = $1.30 * 14
    Staircase cost = $18.20

    Subtract this from the cost of the total cleaning bill of $253.95. We do this to isolate the cost of the carpet.
    Carpet cost = $253.95 - $18.20
    Carpet cost = $235.75

    Now, the remaining carpet cost can be written as:
    75 + $0.25(s - 180) = $235.75 <-- were s is the total square foot of carpet cleaned

    Multiply through and simplify:
    75 + 0.25s - 45 = $235.75

    Combine like terms:
    0.25s + 30 = 235.75

    Type this equation into our search engine to solve for s, and we get:
    s = 823
     

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