Let their ages be as follows:

Tom's age = T

Bob's age = B

Joe's age = J

==> Given that the sum of their ages is 47

==> T + B + J = 46 ..........(1)

Also, given that Joe was born 3 years before Bob, then, Joe is...

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Let their ages be as follows:

Tom's age = T

Bob's age = B

Joe's age = J

==> Given that the sum of their ages is 47

==> T + B + J = 46 ..........(1)

Also, given that Joe was born 3 years before Bob, then, Joe is 3 years older than Bob.

==> J = B + 3 ................(2)

Also, Joe was born 4 years after Tom, then, Tom is 4 years older than Joe

==> T = J + 4 ..................(3)

Now we will substitute (2) into (3).

==> T = (B+3) + 4

==> T = B + 7 ..................(4)

Now we will substitute (2) and (4) into (1).

==> T + B + J = 46

==> (B+7) + B + (B+3) = 46

==> 3B + 10 = 46

==> 3B = 36

==> B = 36/3 = 12

==> T= B+7 = 12+7 = 19

==> J = B+3 = 12+3 = 15

**Then, Bob is 12, Joe is 15, and Tom is 19.**

==> 12+15 + 19 = 46.