Question 284834
Tom owns 2,000 shares of company X and 10,000 shares of company Y for a total value equal to $372,000.


Tim owns 8,000 shares of company X and 6,000 shares of company Y for a total value equal to $400,000.


Let a equal the value of each share of company X.


Let b equal the value of each share of company Y.


For Tom:


2,000 * a + 10,000 * b = 372,000.


For Tim:


8,000 * a + 6,000 * b = 400,000.


Since the value of each share in company X and company Y is the same, then a and b must be the same values in both equations.


To find that value, solve the 2 equations simultaneously.


The 2 equations that need to be solved simultaneously are:


2,000 * a + 10,000 * b = 372,000.
8,000 * a + 6,000 * b = 400,000.


Multiply the first equation by 4 to get:


8,000 * a + 40,000 * b = 1,488,000.
8,000 * a + 6,000 * b = 400,000


Subtract second equation from first equation to get:


34,000 * b = 1,088,000


Divide both sides of this equation by 44,000 to get:


b = 32 dollars per share.


Substitute for b in the first original equation to get:


2,000 * a + 10,000 * b = 372,000 becomes:


2,000 * a + 10,000 * 32 = 372,000


Solve for a to get:


a = 26 dollars per share.


You have:


a = 26 dollars per share.
b = 32 dollars per share.


Substitute in both original equations to get:


2,000 * a + 10,000 * b = 372,000.
8,000 * a + 6,000 * b = 400,000.


become:


2,000 * 26 + 10,000 * 32 = 52,000 + 320,000 = 372,000.
8,000 * 26 + 6,000 * 32 = 208,000 + 192,000 = 400,000.


Since the sum of the parts is equal to the original whole, this confirms the values are good.


Your answer is:


The value of the shares of company X is $26.00 per share.


The value fo the shares of company Y is $32.00 per share.