8 years ago Mary was one-half as old as her elder sister. 4 years ago from now, Mary would be two-thirds as old as her elder sister. What is the current age of both Mary and her sister?
+129847 Let x be Mary's age now and y be her elder sister's age now....and we have the following system
2(x -8) = y - 8 → 2x - 16 = y - 8 → y = 2x - 8 (1)
x + 4 = (2/3)(y + 4) (2)
Put (1) into (2) and we have
x + 4 = (2/3) (2x - 8 + 4) multiply both sides by 3
3x + 12 = 2(2x - 4)
3x + 12 = 4x - 8 subtract 3x from both sides......add 8 to both sides
20 = x and this is Mary's age now
y = 2(20) - 8 = 32 and this is her elder sister's age now
Proof :
8 years ago....Mary was 12 and her elder sister was 24......twice as old
4 years from now, Mary will be 24 and her sister will be 36......Mary will be 2/3 rds of her elder sister's age
+129847 Let x be Mary's age now and y be her elder sister's age now....and we have the following system
2(x -8) = y - 8 → 2x - 16 = y - 8 → y = 2x - 8 (1)
x + 4 = (2/3)(y + 4) (2)
Put (1) into (2) and we have
x + 4 = (2/3) (2x - 8 + 4) multiply both sides by 3
3x + 12 = 2(2x - 4)
3x + 12 = 4x - 8 subtract 3x from both sides......add 8 to both sides
20 = x and this is Mary's age now
y = 2(20) - 8 = 32 and this is her elder sister's age now
Proof :
8 years ago....Mary was 12 and her elder sister was 24......twice as old
4 years from now, Mary will be 24 and her sister will be 36......Mary will be 2/3 rds of her elder sister's age
