Solving Quadratic Equations: A Step-by-Step Guide

[TheShapeOfTime]

I was given a bunch of quadratic homework and I'm stuck on a few problems:

"Brendan buys a black of shares for $1895. When the share price goes up by $4/share, he sells all but 15 of them for $1740. How many shares did he buy?"

I got the equation $$\frac{1895}{x} - \frac{1740}{x + 4} = 15$$ but I worked it out and I don't get the answer (~73).

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"A rectangular field has a perimeter 500 m and an area 14 400 m^2. Find the lengths of its sides."

$$l * w = 14 400$$
$$2l + 2w = 500$$
Not sure what to do from here...

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Thanks in advance for any help

 

[arildno]

How on Earth did you get your first equation??
It is, as far as I can see, totally wrong.

Let "P" be the initial price for one share, and "x" the number of shares originally bought.
Then, the information given can be written as:
P*x=1895
(P+4)*(x-15)=1740

We therefore have $$P=\frac{1895}{x}$$
This yields a quadratic in x you can solve.

 

[t!m]

And the second problem you have set up right and is now simply solving a system of linear equations. Solve one of the eqns for one variable ... substitute ... sound familiar?

 

[TheShapeOfTime]

And the second problem you have set up right and is now simply solving a system of linear equations. Solve one of the eqns for one variable ... substitute ... sound familiar?

Yeah, I had worked it out like that earlier and didn't get the right answer, but I realize now it was just a dumb mistake.

There is one last part of a question I can't get:

"Given $kx^2+(k+3)x+(3-4k) = 0$. Find the value of k if
c) one of the roots is 2"

Thanks for your help, both of you.

 

[HallsofIvy]

Notice that in the first equation you gave:$$\frac{1895}{x} - \frac{1740}{x + 4} = 15$$, The numerator of each fraction on the left is an amount of money: dollars, while the denominator is the number of shares bought: each fraction is "dollars per share".

Actually, that's not quite correct because I assume you got the "4" from "$4/share" and you can't add "shares" to "dollars per share". You CAN subtract "shares" from "shares", of course, so I feel sure that what you intended was the second denominator to be "x- 15": the number of shares less the number NOT sold: the number of shares sold. Of course, then, the right hand side of the equation must also be in "dollars per share": $4/share would work nicely. Looks to me like the equation you intended to write was $$\frac{1895}{x} - \frac{1740}{x -15} = 4$$.
Solve that for x.

 

[TheShapeOfTime]

Notice that in the first equation you gave:$$\frac{1895}{x} - \frac{1740}{x + 4} = 15$$, The numerator of each fraction on the left is an amount of money: dollars, while the denominator is the number of shares bought: each fraction is "dollars per share".

Actually, that's not quite correct because I assume you got the "4" from "$4/share" and you can't add "shares" to "dollars per share". You CAN subtract "shares" from "shares", of course, so I feel sure that what you intended was the second denominator to be "x- 15": the number of shares less the number NOT sold: the number of shares sold. Of course, then, the right hand side of the equation must also be in "dollars per share": $4/share would work nicely. Looks to me like the equation you intended to write was $$\frac{1895}{x} - \frac{1740}{x -15} = 4$$.
Solve that for x.

You're right, that was what I was going for. I had a typo in it earlier (x + 1 instead of x + 4), which was what made arildno react the way he did :p

 

[arildno]

You're right, that was what I was going for. I had a typo in it earlier (x + 1 instead of x + 4), which was what made arildno react the way he did :p

Yeah, I guess I overreacted a bit. Sorry..