Question 781361
Start by creating equations using all of the known info from the problem.

For ease of use, let's use each person's initial as their variable.
B = Bill
H = Henry
S = Sam
R = Rob
J = Jane

Henry is two times older than Bill can be expressed as H = 2 x B or H = 2B
Sam is two years older than Henry can be expressed as S = H + 2
Rob is three times Bill's age can be expressed as R = 3 x B or R = 3B
Jane is one year younger than Rob can be expressed as J = R - 1
The sum of their ages is 45 can be expressed as 45 = H + S + R + J + B

Now to solve, you must find a way to combine "like" variables as follows:

H = 2B
S = H + 2
You can substitute 2B for H in S = H + 2 to get S = 2B + 2
Then
R = 3B
J = R - 1
Again, as above, you can substitute 3B for R in J = R - 1 to get J = 3B - 1
And finally,
45 = H + S + R + J + B becomes 45 = 2B + (2B + 2) + 3B + (3B - 1) + B

To solve, simplify and combine like terms as follows:
45 = 2B + (2B + 2) + 3B + (3B - 1) + B
becomes
45 = (2B + 2B + 3B + 3B + B) + (2 - 1)
45 = 11B + 1

Now solve for B.  To do so, you must get B to stand alone by operating on both sides of the equation thereby keeping both sides equal.
45 = 11B + 1
45 - 1 = 11B + (1 - 1)
44 = 11B + 0
44 = 11B
44/11 = 11B/11
4 = B

Now go back to your starting equations and using the known variable B, solve all the equations as follows:
B = 4, therefore Bill is 4 years old
H = 2B becomes  H = 2 x 4 = 8, therefore Henry is 8 years old.
S = 2B + 2 becomes S = 2 x 4 + 2 = 10, therefore Sam is 10 years old.
R = 3B becomes R = 3 x 4 = 12, therefore Rob is 12 years old.
J = 3B - 1 becomes J = 3 x 4 - 1 = 11, therefore Jane is 11.
And finally, to check your answer, insert all the ages and make sure they total up 45.
45 = 8 + 10 + 12 + 11 + 4