Question 284834: suppose tom owns 2,000 shares of company X and 10,000 shares of company Y. The total value of tom's holdings of these two companies is $372,000.
Suppose tim owns 8,000 shares of company X and 6,000 of company Y. total value holdings is $400,000
write an equation for tom and tim's holdings. use variables X and Y to represent the value of shares of company X and company Y then need to show the value of share of company X and Y
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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