SOLUTION: The total of Xanthe's, Yarrow's, and Zeke's ages is 51. Five years from now Yarrow will be the same age as Zeke is now. Six years ago, Yarrow's age was half of Xanthe's age. How ol

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Question 214858: The total of Xanthe's, Yarrow's, and Zeke's ages is 51. Five years from now Yarrow will be the same age as Zeke is now. Six years ago, Yarrow's age was half of Xanthe's age. How old is each now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
(1) x+%2B+y+%2B+z+=+51
(2) y+%2B+5+=+z
(3) y+-+6+=+x%2F2
----------------
from (3)
(3) 2y+-+12+=+x
Substitute (2) and (3) in (1)
2y+-+12+%2B+y+%2B+y+%2B+5+=+51
4y+-+7+=+51
4y+=+58
y+=+14.5
(2) y+%2B+5+=+z
14.5+%2B+5+=+z
z+=+19.5
(3) 2y+-+12+=+x
2%2A14.5+-+12+=+x
x+=+29+-+12
x+=+17
Xanthe is 17, Yarrow is 14.5, Zeke is 19.5
Check answer:
(1) x+%2B+y+%2B+z+=+51
17+%2B+14.5+%2B+19.5+=+51
51+=+51
and
(2) y+%2B+5+=+z
14.5+%2B+5+=+19.5
19.5+=+19.5
and
(3) y+-+6+=+x%2F2
14.5+-+6+=+17%2F2
29+-+12+=+17
17+=+17
OK