SOLUTION: I am having extreme troubles solving this math problem Part II: Solving Inequalities Your company needs to temporarily hire a programmer to work on a project. Two proposed pa

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Question 548042: I am having extreme troubles solving this math problem
Part II: Solving Inequalities
Your company needs to temporarily hire a programmer to work on a project. Two proposed payment schemes for this work are as follows:
(1) A flat fee of $1,000, plus $20 per hour or (2) $25 per hour.
For each of the two plans, show an expression that can be used to compute the amount of pay for that plan. The variable should be the number of hours worked.
Set up and solve an inequality that would enable your company to determine possible job lengths (in hours) for which the person is paid less according to plan 1 than for plan 2.
Interpret the solution of the inequality in terms of which is better for your company.
Part III: Functions and Graphing
From Part II, express each of the two pay plans as a function of the number of hours worked (again, the variable represent the number of hours. Graph both functions.

Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website!
PART II
Let x be the number of hours worked. Let y be the cost, in $.
For plan (1)
For plan (2)
Those are the expressions you can use to calculate cost (y) as a function of hours worked (x).
If the cost for plan 1 must be less than the cost for plan 2, we can set up the inequality

We can solve that inequality by subtracting from both sides to get
and then dividing both sides by 5 to get

So if you think the job will probably take more than 200 hours, use plan 1.
The lower hourly rate of $20 instead of $25, will more than offset the $1000 up-front fee, if the job takes more than 200 hours.
PART III
We have the functions from Part II above:
For plan (1)
For plan (2)
Those are the equations for two straight lines.
The graph should look like this