Question 236084: 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 $340,000.
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 $340,000.
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 Theo(13342)   (Show Source):
You can put this solution on YOUR website! Bob owns 2000*x + 10000*y = 340000
Frank owns 8000*x + 6000*y = 340000
If we solve these equations simultaneously, then we should get the value of each share.
your equations are:
2000x + 10000y = 340000
8000x + 6000y = 340000
there are 3 ways to solve this equation simultaneously.
1 is by substitution.
2 is by elimination.
3 is by setting the equations the left side of each equation equal to each other because they are both equal to 340000.
we'll use elimination.
the equations are:
2000x + 10000y = 340000 (equation 1)
8000x + 6000y = 340000 (equation 2)
multiply the first equation by 4 to get:
8000x + 40000y = 1360000 equation 3)
8000x + 6000y = 340000 (equation 2)
subtract equation 2 from equation 3 to get:
34000y = 1020000
solve for y to get:
y = 1020000/34000 = 30
replace y with 30 in equation 1 to get:
2000x + 10000y = 340000 (equation 1) becomes:
2000x + 10000*30 = 340000 which becomes:
2000x + 300000 = 340000
subtract 300000 from both sides to get:
2000x = 340000 - 300000 which becomes:
2000x = 40000
divide both sides by 2000 to get:
x = 20
you have:
x = 20
y = 30
substitute in both original equations to confirm the answer is good for both equations simultaneously.
2000x + 10000y = 340000 (equation 1)
8000x + 6000y = 340000 (equation 2)
become:
2000*20 + 10000*30 = 340000
8000*20 + 6000*30 = 340000
these become:
40000 + 300000 = 340000
160000 + 180000 = 340000
these become:
340000 = 340000
340000 = 340000
both equations are true which means that the answer provided are good.
your answers are:
x = 20 (each share of company x = $20.00)
y = 30 (each share of company y = $30.00)
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