SOLUTION: the sum of 3 nos is 24 among them 1number is equal to half of the sum of other 2 nos but four times the difference of them find the numbers

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Question 421854: the sum of 3 nos is 24 among them 1number is equal to half of the sum of other 2 nos but four times the difference of them find the numbers
Answer by mananth(16946) About Me  (Show Source):
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let the numbers be x y z
x+y+z=24
x=1/2(y+z)
2x=y+z
2x-y-z=0
x=4(y-z)
x=4y-4z
x-4y+4z=0
....
x+y+z=24 --------------1
2x-y-z= 0-------------2
x-4y+4z= 0-------------3
..
consider equation 1 &2
Multiply 1 by 1
Multiply 2 by 1
we get
x+y+z=24
2x-y-z=0
Add the two
3x=24 -------------4
consider equation 2 & 3
Multiply 2 by -4
Multiply 3 by 1
we get
-8x+4y +4z=0
x-4y+4z =0
Add the two
-7x+8z=0 -------------5
Consider (4) & (5)
Multiply 4 by 7
Multiply (5) by 3
we get
21x=168
-21x+24z =0
Add the two
24z=168
/24
z=7
Plug the value of z in 5
-7x+56=0
-7x=-56
x=8
plug value of x & z in 1
8+y+7=24
y=-8-7+24
y=9