SOLUTION: An investor bought 600 shares of stock, some at $5.75 per share and some at $7.00 per share. If the total cost was $4,075.00, how many shares of each stock did the investor buy?

Question 903439: An investor bought 600 shares of stock, some at $5.75 per share and some at $7.00 per share. If the total cost was $4,075.00, how many shares of each stock did the investor buy?
Found 2 solutions by richwmiller, AlgebraLady88:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
m+p=600,
5.75*m+7*p=4075
m=600-p
5.75*(600-p)+7*p=4075
3450.0-5.75p+7*p=4075
1.25*p=625.0
p=500.0
m=600-p
m=100 at $5.75 and p=500 at $7
check
100+500=600
5.75*m+7*p=4075
5.75*100+7*500=4075
575.0+3500=4075
4075.0=4075
ok

Answer by AlgebraLady88(44) (Show Source): You can put this solution on YOUR website!
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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