A person has $27000 nvested in stock A and stock B. Stock A currently sells for $30 a share and stock B sells for $80 a share. If stock B triples in value and stock A goes up 50%, his stock will be worth $76 comma 500. How many shares of each stock does he own?

Step-by-step explanation:

Let x be initial number of shares of stock A and y be the initial number of shares of stock B.

Since the cost of one share of stock A is $30, the cost of x shares would be $ 30x. Similarly, the cost of y shares of stock B would be $ 80y.

The person bought these x and y shares in $ 27,000. So we can set up the equation as:

30x + 80y = 27000 Equation 1

Value of stock B triples. So new value of each share of stock B would be $ 240 and the price of y shares will be $ 240y. Value of stock A goes up by 50%. This means the price of each share of stock A would be 30 + 0.5 (30) = $ 45 and the price of x shares would be $ 45x.

The worth of stock increased to $ 76,500. So we can set up the equation as:

45x + 240y = 76500 Equation 2

Multiplying Equation 1 by 1.5 and subtracting from Equation 2, we get:

45x + 240y - 1.5 (30x + 80y) = 76500 - 1.5 (27000)

45x + 240y - 45x - 120y = 36000

120y = 36000

y = 300

Using the value of y in Equation 1, we get:

30x + 80 (300) = 27000

30x = 27000 - 80 (300)

30x = 3000

x = 100

This means the person bough 100 shares of stock A and 300 shares of stock B.