Question 263280: Given the equations 3x + y = 17, 5y + z = 14 and 3x + 5z = 41, what is the value of the sum x + y + z?
Found 3 solutions by mananth, richwmiller, ikleyn:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! Given the equations 3x + y = 17, 5y + z = 14 and 3x + 5z = 41, what is the value of the sum x + y + z?
3x + y = 17, ---------------1
5y + z = 14 ----------------2
3x + 5z = 41, ---------------3
Multiply eq1 by5 and subtract 2 from it
15x+5y=85
5y+z=14
15x-z=71
Multiply eq 3 by 5 and solve with the above
15x+25z=205
-26z=- 134
Z= 5.15
Y=1.77
X= 5.08
Answer by richwmiller(17219)  (Show Source):
Answer by ikleyn(53727)  (Show Source):
You can put this solution on YOUR website! .
Given the equations 3x + y = 17, 5y + z = 14 and 3x + 5z = 41, what is the value of the sum x + y + z?
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There is a way much shorter and much more elegant to solve the problem
than the method used by @mananth.
See my solution below.
Your starting equations are
3x + y = 17,
5y + z = 14 ,
3x + 5z = 41.
Add all three equations. You will get
6x + 6y + 6z = 17 + 14 + 41,
or
6(x + y + z) = 72.
Divide both sides by 6
x + y + z = 72/6 = 12.
At this point, the problem is just solved completely.
ANSWER. x + y + z = 12.
Solved in the shortest way.
I am 129% sure that the true meaning and the destination of this problem
is to teach you to solve it by this short and elegant method.
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