Question

QuestionsMar 17, 3:07:06 PMBrayden is working two summer jobs, making $18 per hour lifeguarding and making$9 per hour clearing tables. In a given week, he can work no more than 19 total hoursand must earn a minimum of $270. If Brayden worked 14 hours lifeguarding,determine the minimum number of whole hours clearing tables that he must work tomeet his requirements. If there are no possible solutions, submit an empty answer.Answer:Submit Answeror

Answer 1

The minimum number of hours he can spend cleaning the table is 2 hours

Here, we want to calculate the minimum number of whole hours clearing tables that must be worked

Let the number of hours spent lifeguarding be l, while the number of hours spent clearing tables be t

The total number of hours is 19 hours maximum

Thus, we have it that;

$l\text{ + t}\leq\text{ 19}$

Secondly, he must earn a minimum of $270

So, if we have the product of the number of hours and the payment per hour for each job, the amount must be at least $270

Mathematically, we have this as;

$18l\text{ + 9t }\leq\text{ 270}$

From the question, we are told that he spent 14 hours life-guarding

Since the total number of hours cannot be greater than 19, it means that the number of hours spent cleaning the table is between 1 and 5 (maximum)

Now, let us use these values and see if the arrangement will work

We plug the value of 14 for the number of hours spent lifeguarding into the second equation, while we switch values for the number of hours spent cleaning tables from 1-5

We have this as;

$\begin{gathered} 18(14)\text{ + 9(5) = 297} \\ 18(14)\text{ + 9(4) = 288} \\ 18(14)\text{ + 9(3) = 279} \\ 18(14)\text{ + 9(2) = 270} \\ 18(14)\text{ + 9(1) = 261} \end{gathered}$

As we can see, only the time for two hours gave the lowest possible amount of what he can earn for the second equation to be correct

Hence, the minimum number of hours he must spend cleaning the table is 2 hours