Answer:
M=9
EXPLANATION:
Let R represent Ronald’s present age. Let M represent Miley’s present age. Three years from now, Ronald and Miley will be R+3 and M+3 years old, respectively.
Your assertion “Three years from now, Ron’s age will be 2 times that of Miley's” can be written as
R + 3 = 2*(M + 3)
Similarly, your assertion “Three years ago, Ron's age was 3 times that of Miley's” can be written as
R - 3 = 3*(M-3)
We can add the left side of these equations together, and also the right side of these equations together, and obtain a new equation …
R + 3 + R - 3 = 2*(M + 3) + 3*(M - 3) = 2M + 6 + 3M - 9 = 5M - 3
This can be simplified to
2R = 5M - 3
We can divide both sides of the last equation by 2, and obtain ..
(2/2) * R = (5/2) * M - 3/2, or R = (5/2) * M - 3/2.
Now we can “plug in” the last equation into either of our first two equations of this post, and solve for M.
Using the first equation, we have
(5/2) * M - 3/2 + 3 = 2 *(M + 3) = 2M + 6
We now have
(5/2) * M + 3/2 = 2M + 6
The left side of this equation can be rewritten as
(5M + 3) / 2, so we obtain
(5M + 3) / 2 = 2M + 6
Multiplying both sides by 2, we have
5M + 3 = 4M + 12
Subtracting 4M and 3 from both sides, we obtain
M = 9
Miley’s present age is 9.
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