For a project in statistics class, a pair of students decided to invest in two companies, one that produces software and one that does biotechnology research. Dean purchased 14 shares in the software company and 14 shares in the biotech firm, which cost a total of $812. At the same time, Carrie invested a total of $5,767 in 100 shares in the software company and 99 shares in the biotech firm. How much did each share cost?

The cost of each share in the software company is $25 and the cost price each share in biotechnology is $33.

Step-by-step explanation:

Let The cost of each share in the software company be = x

and each share in biotechnology be = y

The cost price of 14 shares in the software company and 14 share in biotechnology is = 14x+14y

The cost price of 100 shares in the software company and 99 share in biotechnology is = 100x + 99y

According to the problem,

14x + 14y = 812

⇔x+y = 58 ... (1)

and

100x + 99y=5767 ... (2)

Equation (1) * 100 - Equation (2)

100x + 100y - (100x+99y) = 5800-5767

⇔100x + 100 y - 100x-99y=33

⇔y=33

putting the value of y in equation (1)

x+33=58

⇔x=58-33

⇔x=25

The cost of each share in the software company is$25 and the cost price each share in biotechnology is $33.