Aperson 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.

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