# 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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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