SOLUTION: I need to determine x, y and z when x+y+z=1150 and x=4z-100 and x=6y+50. So far the only thing I have figured out is that 1150=1150. Not a good answer. Can someone please he

Algebra ->  Equations -> SOLUTION: I need to determine x, y and z when x+y+z=1150 and x=4z-100 and x=6y+50. So far the only thing I have figured out is that 1150=1150. Not a good answer. Can someone please he      Log On


   



Question 168385: I need to determine x, y and z when x+y+z=1150 and x=4z-100 and x=6y+50. So far the only thing I have figured out is that 1150=1150. Not a good answer.
Can someone please help.

Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
determine x, y and z when
x+y+z=1150
x=4z-100
x=6y+50
-------------
x + y + z = 1150
x + 0 -4z = -100
x -6y + 0 = 50
--------------------
Use any method to solve the system to get:
x = 800
y = 125
z = 225
=================
Cheers,
Stan H.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There are 3 equations and 3 unknowns, so
it should be solvable
(1) x+%2B+y+%2B+z+=+1150 given
(2) x+=+4z+-+100 given
(3) 4z+=+x+%2B+100
(4) z+=+%281%2F4%29%2Ax+%2B+25
(5) x+=+6y+%2B+50 given
(6) 6y+=+x+-+50
(7) y+=+%281%2F6%29%2Ax+-+25%2F3
Now substitute (4) and (7) into (1)
(8) x+%2B+%281%2F6%29%2Ax+-+25%2F3+%2B+%281%2F4%29%2Ax+%2B+25+=+1150
Multiply both sides by 12
(9) 12x+%2B+2x+-+100+%2B+3x+%2B+300+=+13800
(10) 17x+=+13600
x+=+800
And from (4)
(4) z+=+%281%2F4%29%2Ax+%2B+25
(11) z+=+%281%2F4%29%2A800+%2B+25
(12) z+=+225
And from (7)
(7) y+=+%281%2F6%29%2Ax+-+25%2F3
(13) y+=+%281%2F6%29%2A800+-+25%2F3
(14) y+=+%282%2A800+-+4%2A25%29+%2F+12
(15) y+=+1500%2F12
(16) y+=+125
The answers are x = 800, y = 125, z = 225
check answers:
(1) x+%2B+y+%2B+z+=+1150 given
(2) x+=+4z+-+100 given
(5) x+=+6y+%2B+50 given
--------------------------------
(1) x+%2B+y+%2B+z+=+1150
(17) 800+%2B+125+%2B+225+=+1150
(18) 1150+=+1150
--------------------------------
(2) x+=+4z+-+100
(19) 800+=+4%2A225+-+100
(20) 800+=+800
--------------------------------
(5) x+=+6y+%2B+50 given
(21) 800+=+6%2A125+%2B+50
(22) 800+=+800
OK