Word Problem

Question

A person as $30,000 invested in stock A and stock B. Stock A currently sells for $40 a share and stock B sells for $90 a share. If stock B triples in value and stock A goes up 50% his stock will be worth $72,000. How many share of each stock does he own?

Answer 1

First, define your variables.

Let x = number of shares of stock A

Let y = number of shares of stock B

 

Now, use the information given to set up equations.

 

What we know:

 

price of stock A + price of stock B = $30,000

triple the price of stock B + (the price of stock A + 50%) = $72,000

 

price of stock A = # of shares of A * price per share = x * 40 = 40x

price of stock B = # of shares of B * price per share = y * 90 = 90y

 

triple the price of stock B = 90*3 = 270

the price of stock A + 50% = 40 + .5(40) = 60

 

Using this, we get these two equations:

 

40x + 90y = 30,000

60x + 270y = 72,000

 

Now, we can solve the system of equations for x and y.

 

First, multiply the first equation by -3 and add it to the second to eliminate y.

 

-3(40x + 90y = 30,000) => -120x - 270y = -90,000

 

-120x - 270y = -90,000

+60x + 270y = 72,000

___________________

-60x  + 0y    = -18,000

 

Next, divide each side by -60 to isolate x.

 

-60x = -18,000

-60         -60

 

x = 300

 

Next, plug x into either one of the initial equations to find y.

 

40(300) + 90y = 30,000

12000 +90y = 30,000

-12,000           -12,000    subtract 12,000 from each side

90y = 18,000

90          90                       divide both sides by 90 to isolate y

 

y = 200

 

Finally, find the answer to the question asked: How may shares of each stock does he own?

 

He owns 300 shares of stock A and 200 shares of stock B.

 

Answer 2

Let x = # of shares of stock a

Let y = number of shares of stock b

 

We know that

40x + 90y = 30000

and

60x + 270y = 72000 (when stock a increases by 50% and stock b triples

 

We have 2 linear equations and 2 unknowns.

Solve using the addition method

 

40x + 90y = 30000

60x + 270y = 72000

 

Multiply the 1st equation by 3

120x + 270y = 90000

60x + 270y = 72000

subtract the second from the first

 

60x = 18000

x = 300

Plugging this back in to the first equation

 

12000 + 90y = 30000

90y = 18000

y = 200

 

And these numbers are verified in the second equation as well.

 

So # of shares of a = 300

     # of shares of b = 200