Question

A person has $28,000 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 triples in value and stock A goes up 50%, his stock will be worth $69,000. How many shares of each stock does he own? The person owns shares of stock A and shares of stock B.

Answer 1

Solution :-

Let x = # of shares of stock a

Let y = number of shares of stock b

We know that

50x + 60y = 28000

and

75x + 180y = 69000 (when stock a increases by 50% and stock b triples

We have 2 linear equations and 2 unknowns.

Solve using the addition method

50x + 60y = 28000

75x + 180y = 69000

Multiply the 1st equation by 3

150x + 180y = 84000

75x + 180y = 69000

subtract the second from the first

75x = 15000

x = 200

Plugging this back in to the first equation

10000 + 60y = 28000

60y = 18000

y = 300

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

So # of shares of a = 200

     # of shares of b = 300

The person owns 200 shares of stock A and 300 shares of stock B.