Answer:
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.
