SOLUTION: Fe, her mother and grandmother has an average age of 53, one-half of her grandmother's age, plus one- third of her mother's age, plus one-forth of her age is 65. if four years ago,

Question 785762: Fe, her mother and grandmother has an average age of 53, one-half of her grandmother's age, plus one- third of her mother's age, plus one-forth of her age is 65. if four years ago, Fe's grandmother was four times as old as Fe, how old are the now?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Fe, her mother and grandmother has an average age of 53, one-half of her grandmother's age, plus one- third of her mother's age, plus one-forth of her age is 65. if four years ago, Fe's grandmother was four times as old as Fe, how old are the now?
fe-----------------x years
mother-------------y years
GM-----------------z years
(x+y+z)/3=53
x+y+z=159...............................(1)

multiply by 12
6z+4y+3x=780.............................(2)
(z-4)= 4(x-4)
z-4 = 4x-16
4x-z=12.....................................(3)
1 x + 1 y + 1 z = 159 -------------- 1
3 x + 4 y 6 z = 780 -------------- 2
4 x + 0 y + -1 z 12 -------------- 3

consider equation 1 &2 Eliminate y
Multiply 1 by -4 -5
Multiply 2 by 1 4
we get
-4 x + -4 y + -4 z = -636
3 x + 4 y + 6 z = 780
Add the two we get
-1x+2z = 144 ------------- (4)
4x-z=12
-4x+8z=576 ( multiply (4) by 4)
4x-z=12
7z=588
z=84.......... grand mother's age
plug z in (3)
4x-z=12
4x-84=12
4x=96
x=24 ..... Fe's age
x+y+z=159
24+84+y=159
y=159-108
y= 51 ........... mother's age

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