Question 781361: Can you walk me through this word problem, and help me find the solution?
Henry is two times older than Bill. Sam is two years older than Henry, and Rob is three times Bill's age. Jane is one year younger than Rob. The sum of their ages is 45. Find each of the ages.
Answer by amazingrace333(11)   (Show Source):
You can put this solution on YOUR website! 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
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