Question

Anand needs to hire a plumber. He's considering a plumber that charges an initial fee of $65 along with an hourly rate of $28. The plumber only charges for a whole number of hours. Anand would like to spend no more than $250, and he wonders how many hours of work he can afford. Let H represent the whole number of hours that the plumber works.1) wich inequality describes this scenario?2) What is the largest whole number of hours that anand can afford?

Answer 1

Let H represent the whole number of hours that the plumber works.

We were told that he's considering a plumber that charges an initial fee of $65 along with an hourly rate of $28. This means that if he hires this plumber for H hours, the expression for the total cost would be

65 + 28H

Anand would like to spend no more than $250. This means that the amount that he wnats to spend is lesser than or equal to $250.

1) If he hires the plumber, the inequality that describes this scenario would be

`65\text{ + 28H }\leq250`

2) We would solve for H. It becomes

`\begin{gathered} 65\text{ + 28H }\leq250 \\ 28H\text{ }\leq250\text{ - 65} \\ 28H\text{ }\leq185 \\ H\text{ }\leq(185)/(28) \\ H\leq6.61 \end{gathered}`

Since the number of hours must be whole numbers, then the largest whole number of hours that anand can afford is 6 hours. This is so because the next whole number is 7 hours and that would be more than he can afford