SOLUTION: A broker bought shares at a cost of 18759. He reserved 15 shares and sold the rest for 17400 making a gain of 40 per share. How many shares did he buy?

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Question 482164: A broker bought shares at a cost of 18759. He reserved 15 shares and sold the rest for 17400 making a gain of 40 per share. How many shares did he buy?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let s=number of shares
gross profit - profit of the reserved shares = 17400
(18759+40s)-15((18759+40s)/s)=17400
(18759+40s)-((281385+600s)/s)=17400
18759s+40s^2-281385-600s=17400s
40s^2+759s-281385=0
s^2+19s-7035
s=74.9 shares. (see below)
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Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B19x%2B-7035+=+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=%2819%29%5E2-4%2A1%2A-7035=28501.

Discriminant d=28501 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-19%2B-sqrt%28+28501+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2819%29%2Bsqrt%28+28501+%29%29%2F2%5C1+=+74.9111959398752
x%5B2%5D+=+%28-%2819%29-sqrt%28+28501+%29%29%2F2%5C1+=+-93.9111959398752

Quadratic expression 1x%5E2%2B19x%2B-7035 can be factored:
1x%5E2%2B19x%2B-7035+=+1%28x-74.9111959398752%29%2A%28x--93.9111959398752%29
Again, the answer is: 74.9111959398752, -93.9111959398752. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B19%2Ax%2B-7035+%29