SOLUTION: A student did a word-processing job for $10. It took him 8 hours longer than he expected, and therefore he earned $4 per hour less than he anticipated. How long did he expect that

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A student did a word-processing job for $10. It took him 8 hours longer than he expected, and therefore he earned $4 per hour less than he anticipated. How long did he expect that       Log On


   

Question 628788: A student did a word-processing job for $10. It took him 8 hours longer than he expected, and therefore he earned $4 per hour less than he anticipated. How long did he expect that it would take to do the job?
Answer by graphmatics(170) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the number of hours he anticipated working. Let y be the hourly wage he anticipated. He anticipated making $10 for the job. xy=10 (x+8)(y-4)=10
y=10/x (x+8)(10/x-4)=10
x(x+8)(10/x-4)=10x (x+8)(10-4x)=10x 10x-4*x*x+80-32x=10x -4*x*x-32x+80=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -4x%5E2%2B-32x%2B80+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-32%29%5E2-4%2A-4%2A80=2304.

Discriminant d=2304 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--32%2B-sqrt%28+2304+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-32%29%2Bsqrt%28+2304+%29%29%2F2%5C-4+=+-10
x%5B2%5D+=+%28-%28-32%29-sqrt%28+2304+%29%29%2F2%5C-4+=+2

Quadratic expression -4x%5E2%2B-32x%2B80 can be factored:
-4x%5E2%2B-32x%2B80+=+-4%28x--10%29%2A%28x-2%29
Again, the answer is: -10, 2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4%2Ax%5E2%2B-32%2Ax%2B80+%29

He anticipated working 2 hours.