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?

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) (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)
.
Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=28501 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 74.9111959398752, -93.9111959398752. Here's your graph:

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