Question 236084
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)