Question 903439
We can tackle this type of question step by step, which would be less confusing and daunting .
So, the first statement is that ," an investor bought 600 shares of stock, some at $5.75 per share and some at $7.00 per share."

Right off we know how many stocks he bought and that he bought two types. We can write this out as

x+y = 600 

'x' for one type and 'y' for the other.
Now, wasn't that easy? 

Now , the next statement tells us that the total cost was $4075.00 and the question concerns how many shares of each stock the investor bought.

This again can be written as :

5.75 x + 7.00 y = 4075

We don't know how many 'x' stocks and how many 'y' stocks he bought. That's what we are trying to find out.

We now have two equations:

x+y = 600               (a)
5.75 x+ 7.00 y= 4075    (b)

We will use the process of elimination. In (a) we will multiply each by -7
to get

-7x-7y = -4200          (c)

Now, we will add equations (b) and (c)
and get

-1.25 x=  - 125
      x=  100
That means, y= 500 based on equation (a)

To check:

We will plug in numbers into equation (b)

5.75 x + 7 y= 4075
5.75 (100) + 7 ( 500) = 4075  Voila!

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