SOLUTION: A worker charges $30 for a 2 hour job. He charges $94 for a 4 hour job. How much would he charge for an 8 hour job?

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Question 57512This question is from textbook
: A worker charges $30 for a 2 hour job. He charges $94 for a 4 hour job. How much would he charge for an 8 hour job? This question is from textbook

Answer by hayek(51) About Me  (Show Source):
You can put this solution on YOUR website!
Well, there are an infinite number of answers to this one, if there are no other constraints to the question. But, if you assume that the worker's price is a linear function of the time he spends on the job, then the general formula would be:
highlight%28P=a%2At%2Bb%29, where P is total price and t = time.
We have two unknowns, a and b, and two data points, so plug them in and generate two equations:
Eq. 1: $30 for a 2 hour job==> 30=a%2A2%2Bb
Eq. 2: $94 for a 4 hour job==>94=a%2A4%2Bb
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Solve Eq.1 for a:
2%2Aa=30-b
Eq. 3: a=%2830-b%29%2F2
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Plug that result into Eq. 2:
94=%28%2830-b%29%2F2%29%2A4%2Bb
94=60-2b%2Bb
highlight%28b=-34%29
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Plug that into Eq.3 to get a:
a=%2830-%28-34%29%29%2F2
highlight%28a=32%29
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So the formula for price, in terms of time is:
highlight%28P%28t%29=32%2At-34%29
So, for an 8 hour job, the price is: 32%2A8-34=222
.
Here is a graph, note that the formula doesn't make much sense for jobs of less than 1.06 hours.
graph%28300%2C200%2C-1%2C10%2C-25%2C250%2C32%2Ax-34%29