Question 873577: I am aware the same problem has been asked before, but the type of answer requested was different.
The sum of Annie’s, Bert’s and Chris’ ages is 60. Annie is older than Bert by the same number of years that Bert is older than Chris. When Bert is as old as Annie is now,Annie will be three times as old as Chris is now.
1) Use Gaussian elimination to reduce the corresponding augmented matrix to row
echelon form.
Obviously to do so, a system of linear equations must be established.. My problem is that I end up with four variables and then get stuck.
Thankyou!!
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! The sum of Annie’s, Bert’s and Chris’ ages is 60.
x+y+z=60...................(1)
Annie is older than Bert by the same number of years that Bert is older than Chris.
y-z=x-y
2y-z-x=0....................(2)
When Bert is as old as Annie is now,Annie will be three times as old as Chris is now.
the difference between Annies age and Berts age = x-y
(x-y)+y = 3z
x=3z.........................(3)
substitute x=3z in (1) & (2)
x+y+z=60
3z+y+z=60
y+4z=60...................(4)
2y-z-x =0
2y-z-3z=0
2y-4z=0
2y=4z
y=2z
3z+2z+z=60
6z=60
z=10...... Chris
y=2z
y=20...........Bert
x=30.............Annie
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