SOLUTION: Three years ago, Jeffrey was twice as old as Michael is now. In nine years, Jeffery will be four times as old as Michael is now. What are Jeffery's and Michael's current age.

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Question 459136: Three years ago, Jeffrey was twice as old as Michael is now. In nine years, Jeffery will be four times as old as Michael is now. What are Jeffery's and Michael's current age.
Found 2 solutions by oberobic, josmiceli:
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
Start by defining what their ages are now.
J = Jeffrey
M = Michael
.
Three years ago means -3.
Jeffrey was twice as old as Michael is now.
J-3 = 2M
.
In nine year means +9.
J+9 = 4M
.
Set up the linear equations.
J -2M = 3
J - 4M = -9
..
Subtract the second from the first.
2M = 12
M = 6
.
Substitute.
J-3 = 12
J = 15
.
Always check your work!
In this case, use the second equation.
J+9 = 4M
J+9 = 15+9 =24
4M = 4*6 = 24
Right.
.
Answer: Jeffrey is 15, and Michael is 6.
.
Done.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let j = Jeffery's age now
Let m = Michael's age now
Three years ago Jeffery was +j-3+
In nine years Jeffery will be +j+%2B+9+
-----------------------------
given:
(1) +j+-+3+=+2m+
(2) +j+%2B+9+=+4m+
---------------
From (1):
(1) +j+=+2m+%2B+3+
Substitute this in (2)
(2) +2m+%2B+3+%2B+9+=+4m+
(2) +2m+=+12+
+m+=+6+
and
(1) +j+=+2m+%2B+3+
(2) +j+=+2%2A6+%2B+3+
+j+=+15+
Michael is 6 and Jeffery is 15