SOLUTION: Can someone help please? Can these equations be solved? w + x + y + z = 60 w = 1/2(x + y +z) x = 1/3(w + y+ z)

Question 40423: Can someone help please?
Can these equations be solved?
w + x + y + z = 60
w = 1/2(x + y +z)
x = 1/3(w + y+ z)
y = 1/4(w + x + z)
Thanks
geocee
Answer by fazlerabbi(9) (Show Source): You can put this solution on YOUR website!
Given,
w+x+y+z = 60
=> 1/2(x+y+z)+(x+y+z) = 60 ;[As w = 1/2(x+y+z)]
=> 3/2(x+y+z) = 60
=> x+y+z = 40 ;[multiplying both sides by 2/3]

Again
w+x+y+z = 60
=> w+40 = 60 ;[because x+y+z=40]
=> w = 20 ;[subtracting 40 from both sides]
Given
w+x+y+z = 60
=> (w+y+z)+1/3(w+y+z) = 60 ;[given x=1/3(w+y+z)]
=> 4/3(w+y+z) = 60
=> w+y+z = 45 ;[multiplying both sides by 3/4]
Again
w+x+y+z = 60
=> x+45 = 60 ;[because w+y+z = 45]
=> x = 15 ;[subtracting 45 from both sides]
Given
w+x+y+z = 60
=> (w+x+z)+1/4(w+x+z) = 60 ;[given y=1/4(w+x+z)]
=> 5/4(w+x+z) = 60
=> w+x+z = 48 ;[multiplying both sides by 4/5]
Again
w+x+y+z = 60
=> y+48 = 60 ;[because w+x+z = 48]
=> y = 12 ;[subtracting 48 from both sides]
We know,
w+x+y+z = 60
=> 20+15+12+z = 60 ;[as w=20, x=15, y=12]
=> z = 13
The solution is:
w=20, x=15, y=12 and z=13

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