SOLUTION: Robert is 1/2 as old as his father. Twelve years ago he was 1/3 as old as his father was then. Find their present ages

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Question 105932: Robert is 1/2 as old as his father. Twelve years ago he was 1/3 as old as his father was then. Find their present ages
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start by letting R = Robert's present age and F = Father's present age.
From the problem you can write:
1) R+=+%281%2F2%29F "Robert (R) is half as old as his father (F)"
2) R-12+=+%281%2F3%29%28F-12%29 "Twelve years ago, he was 1/3 as old as his father was then"
So now you have a system of equations with two unknowns (R and F) and you can use any of the accepted methods for solving these for R and F.
You can simplify these equations by clearing the fractions.
1) R+=+%281%2F2%29F Multiply through by 2.
1a) 2R+=+F
2) R-12+=+%281%2F3%29%28F-12%29 Multiply through by 3.
2a) 3R-36+=+F-12 Now substitute the F from the simplified equation 1a) into the simplified equation 2a).
3R-36+=+2R-12 Simplify and solve for R by subtracting 2R from both sides.
R-36+=+-12 Add 36 to both sides.
R+=+24 This is Robert's present age.
F+=+2R
F+=+2%2824%29
F+=+48 This is the father's present age.
Check:
R+=+%281%2F2%29F
24+=+%281%2F2%29%2848%29
24+=+24 OK, and...
R-12+=+%281%2F3%29%28F-12%29
24-12+=+%281%2F3%29%2848-12%29
12+=+%281%2F3%29%2836%29
12+=+12 OK