Expert: Scott A Wilson - 12/5/2011

Question
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.

Answer
The 1st job would be 1,000 + 20x, where x is hours.
The 2nd job would be 25x, where x is hours.

To be paid more on job 1, that means that 1,000 + 20x > 25x.
Subtracting 20x from both sides gives 1,000 > 5x.
Dividing both sides by 5 gives 200 > x.
This means that if more than 200 hours of work is scheduled, (1) 1 is better.
If not, (2) is better.  If there are exactly 200 hours of work, both would pay the same.
That is, 1,000 + 20x = 5000 and 25x = 5000 when x = 200.