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?

fe-----------------x years

mother-------------y years

GM-----------------z years

(x+y+z)/3=53
x+y+z=159...............................(1)

{{{z/2 + y/3 + x/4 = 65}}}

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