a cleaning service charges an hourly rate plus a flat fee of $15 for supplies. philip uses the service for 3.5 hours for his spr

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2 years ago

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a cleaning service charges an hourly rate plus a flat fee of $15 for supplies. philip uses the service for 3.5 hours for his spr

ing cleaning, and his total is $232. how can he correctly determine the hourly rate? divide the total cost,$232, by the number of hours,3.5. then, add the flat fee,$15, to the quotient. divide the total cost, 232 dollars by the number of hours, then, add the flat fee, 15 dollars to the quotient. add the supply fee,$15, to the total cost,$232. then, divide the sum by the number of hours,3.5. add the supply fee, 15 dollars to the total cost, then, divide the sum by the number of hours, subtract the supply fee,$15, from the total cost,$232. then, divide the difference by the number of hours,3.5.subtract the supply fee, 15 dollars from the total cost, then, divide the difference by the number of hours, divide the total cost, $232, by the number of hours, 3.5. then, subtract the flat fee, $15, from the quotient.

Mathematics

1 answer:

Sergeu [11.5K] · Answer 1 · 2023-03-07T06:03:43+03:00

Using linear function concepts, it is found that he can correctly determine the hourly rate as follows:

subtract the supply fee, 15 dollars from the total cost, then, divide the difference by the number of hours.

<h3>What is a linear function?</h3>

A linear function is modeled by:

$y = mx + b$

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, which can also be interpreted as the initial value of a function that is valid only for $x \geq 0$ , such as is the case in this problem.

The flat fee is of $15, hence b = 15, then:

$y = mx + 15$

Philip uses the service for 3.5 hours for his spring cleaning, and his total is $232, hence when x = 3.5, y = 232, so we use it to find the hourly rate m.

$y = mx + 15$

$232 = 3.5m + 15$