SOLUTION: Three years ago, Jerri was four times as old as Kelly was then. Five years from now, Jerri will be twice as old as Kelly will be. how old will each one be ten years from now?

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Three years ago, Jerri was four times as old as Kelly was then. Five years from now, Jerri will be twice as old as Kelly will be. how old will each one be ten years from now?      Log On

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Question 697318: Three years ago, Jerri was four times as old as Kelly was then. Five years from now, Jerri will be twice as old as Kelly will be. how old will each one be ten years from now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = Jerri's age now
Let +b+ = Kelly's age now
+a+-+3+ = Jerri's age 3 years ago
+b+-+3+ = Kelly's age 3 years ago
+a+%2B+5+ = Jerri's age 5 years from now
+b+%2B+5+ = Kelly's age 5 years from now
------------------------------------
given:
(1) +a+-+3+=+4%2A%28+b+-+3+%29+
(2) +a+%2B+5++=+2%2A%28+b+%2B+5+%29+
------------------------
(1) +a+-+3+=+4b+-+12+
(1) +a+-+4b+=+-9+
and
(2) +a+%2B+5++=+2%2A%28+b+%2B+5+%29+
(2) +a+%2B+5+=+2b+%2B+10+
(2) +a+-+2b+=+5+
-----------------
Subtract (1) from (2)
(2) +a+-+2b+=+5+
(1) +-a+%2B+4b+=+9+
+2b+=+14+
+b+=+7+
and
(2) +a+-+2b+=+5+
(2) +a+-+2%2A7+=+5+
(2) +a+=+5+%2B+14+
(2) +a+=+19+
-------------
In 10 years, Jerri will be +19%2B10+=+29+
In 10 years Kelly will be +7+%2B+10+=+17+
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check answers
(1) +a+-+3+=+4%2A%28+b+-+3+%29+
(1) +19+-+3+=+4%2A%28+7+-+3+%29+
(1) +16+=+4%2A4+
(1) +16+=+16+
and
(2) +a+%2B+5++=+2%2A%28+b+%2B+5+%29+
(2) +19+%2B+5++=+2%2A%28+7+%2B+5+%29+
(2) +24+=+2%2A12+
(2) +24+=+24+
OK