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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?

 Jan 20, 2016

Best Answer 

 #1
avatar+128079 
+10

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

 

 

 

cool cool cool

 Jan 20, 2016
 #1
avatar+128079 
+10
Best Answer

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

 

 

 

cool cool cool

CPhill Jan 20, 2016
 #2
avatar+153 
0

i agree

 Jan 20, 2016
 #3
avatar+1832 
0

CPhill , In the second equation why did you add 4 ? the question said  4 years ago from now?

 Jan 20, 2016
 #4
avatar
0

Just a grammatical mistake by the questioner.

 Jan 20, 2016

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