SOLUTION: 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

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)

RELATED QUESTIONS
2. Suppose Bob owns 2,000 shares of Company X and 10,000 shares of Company Y. The total... (answered by Mathtut)

2. Suppose Bob owns 2,000 shares of Company X and 10,000 shares of Company Y. The total... (answered by stanbon)

Suppose Bob owns 2,000 shares of Company X and 10,000 shares of Company Y. The total... (answered by jrfrunner)

This is Reginald again with the second question. Suppose Bob owns 8,000 shares of... (answered by DeepaEvangeline)

suppose tom owns 2,000 shares of company X and 10,000 shares of company Y. The total... (answered by Theo)

Suppose Bob owns 2,000 shares of Company X and 10,000 shares of Company Y. The total... (answered by stanbon)

Can you please help me with this problem...Thank you Suppose Bob owns 2,000 shares of... (answered by stanbon)

Answer the question and solve the problems below. Make sure you show all your work so... (answered by JBarnum)

samantha, lauren, and jerry own shares of the same stock with a total value of $7,650. if (answered by stanbon)