SOLUTION: Hello - I need assistance. I have a problem that I can't seem to figure out; please see below, A person has 17,000 invested in stock A and stock B. Stock A currently sells for

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Question 701091: Hello - I need assistance. I have a problem that I can't seem to figure out; please see below,
A person has 17,000 invested in stock A and stock B. Stock A currently sells for $50 a share and stock B sells for $60 a share. If stock B doubles in value and stock A goes up 50%, his stock will be worth $31,500. How many shares of each stock does he own?
Word problems are the worst for me because I am never sure where to start. Once I have the equation I can solve but getting it is the problem. If you can help I would greatly appreciate it.
Thanks.
Found 3 solutions by stanbon, neatmath, DrBeeee:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
A person has 17,000 invested in stock A and stock B. Stock A currently sells for $50 a share and stock B sells for $60 a share. If stock B doubles in value and stock A goes up 50%, his stock will be worth $31,500. How many shares of each stock does he own?
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Quantity Eq: A + B = 17000 stocks
Value Eq: 1.5*50A +2*60B = 31,500 dollars
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Those are the equations you want.
Note; Word Problems are simple if you read carefully.
Just symbolize what the words tell you.
Cheers,
Stan H.

Answer by neatmath(302)   (Show Source):
You can put this solution on YOUR website!

I believe the two equations you would need are:

and

A goes up 50% to 75, B doubles to 120

Using elemination seems to be the easiest method to solve:

Equation 1 multiplied by -2

Add this to the second equation to get:

Then substitue back in Equation 1:

So we have 100 shares of Stock A, and 200 shares of Stock B!

I hope this helps! Keep practicing! :)

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Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website!
ALWAYS define variable(s) to represent each unknown. Then write equations to fit the problem statement. If you have 2 unknowns, as you have, you need two equations.
Let A = the number of shares of stock A
Let B = the number of shares of stock B
Now list the knowns
a) stock A value is $50/share
b) stock B value is $60/share
c) current value of holdings is $17,000
d) some time later stock B doubles to $120/share
e) for the same time, stock A increses by 50% to $75/share
f) after that same time the holdings are worth $31,500
Write the equations for the value of holdings at the current time and for some time later. At the current time his stock is worth
(1) 50*A + 60*B = 17000
And some time later his stock is worth
(2) 75*A + 120*B = 31500
All you need to do is solve (1) and (2) for A and B. You say you can do that, but here's my solution.
First multiply (1) by 2 and get
(3) 100*A + 120*B = 34000
Now subtract (2) from (3) and get
(4) 25*A + 0 = 2500 or
(5) A = 100
Now put A into (1) and get
(6) 50*100 + 60*B = 17000 or
(7) 5000 + 60*B = 17000 or
(8) B = 200
Let's check the answer with (2).
Is (75*100+120*200 = 31500)?
Is (7500+24000 = 31500)?
Is (31500 = 31500)? Yes
Answer: The person owns 100 shares of stock A and 200 shares of stock B.