Question

A contractor has two choices for billing a completed job. · $500 flat rate, regardless of the number of hours worked · $20 per hour worked The graph shows the relationship between pay per hour and number of hours worked for both scenarios. What is the solution to this system of equations, and what does it mean to the contractor?
The solution (0, 20) tells the contractor the minimum amount that can be charged.
The solution (0, 500) tells the contractor the maximum amount that can be charged.
The solution (25, 20) tells the contractor the number of hours on a job where the hourly rate is the same for both billing options.
The solution (20, 25) tells the contractor the number of hours on a job where the hourly rate is the same for both billing options.

Answer 1

The solution to this system of equations is: The solution (25, 20) tells the contractor the number of hours on a job where the hourly rate is the same for both billing options. (Option C).

What does this mean to the contractor?

It means that if the number of hours worked is above 20, then it is more profitable to utilize the $20/hour rate.

What is the explanation for the above?

Recall that the contractor has two options for billing a completed job. They are:

• 500 dollars flat rate
• 20 per work worked

Let us fix x hours to be required for completing the project:

Note that:
The total amount recievable per contract is $500 while working on a retail basis, it will cost $25x.

Stating this mathematically, e have

25x < 500 when x < 20.

This mean that

25x < 500 when x < 20.

Then we find that by I contract he would get 500 $ but by II choice he would get 25x dollars

We find that

25x<500 if x<20

This suggests that a $500 flat rate is preferable if the number of hours done is fewer than 20.

• If the number of hours is greater than 20, the hourly rate, i.e. $20 per hour, is preferable.
• If number of hours is more than 20, hourly rate i.e. 20 per hour is better.

Hence the correct answer is Option C.

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