Question 701091
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.