Question 342379: Suppose Bob owns 2,000 shares of Company X and 10,000 shares of Company Y. The total value of Bob's holdings of these two companies is $372,000.
Suppose Frank owns 8,000 shares of Company X and 6,000 shares of Company Y. The total value of Franks holdings of these two companies is $400,000.
a. Write equations for Bob and Frank's holdings. Use the variables X and Y to represent the values of shares of Company X and Company Y.
b. Solve for the value of a share of Company X and Company Y. Show your work so you can get partial credit even if your final answer is wrong.
Answer by jrfrunner(365)   (Show Source):
You can put this solution on YOUR website! a. Write equations for Bob and Frank's holdings. Use the variables X and Y to represent the values of shares of Company X and Company Y.
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Bob: 2000*x+10000*y=372000
Frank: 8000*x+6000*y=400000
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b. Solve for the value of a share of Company X and Company Y.
1) simplify the equations for Bob and Frank's holdings
2000*x+10000*y=372000 divide both sides by 2000
x+5y=186
8000*x+6000*y=400000 divide both sides by 2000
4x+3y=200
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your new equations are
x+5y=186
4x+3y=200
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multiply first equation by -4
-4x-20y=-744
4x+3y=200
add both equations
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-17y=-544
y=32
substitute this into x+5y=186
x=186-5(32)=26
answer x=26, y=32
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validate
subtitute these value into original equations
Bob: 2000*x+10000*y=372000---> 2000*26+10000*32 does this = 372000??
Frank: 8000*x+6000*y=400000----> 8000*26+6000*32 does this = 400000
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