SOLUTION: Hannah, Mark and Tom have a combined age of 68. Hannah is twice as old as the di erence between Mark and Tom's age. Mark and Tom's combined age is 16 times Hannah's age. Mark is o

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Question 276487: Hannah, Mark and Tom have a combined age of 68. Hannah is twice as old as the di erence between Mark and Tom's age. Mark and Tom's combined age is 16 times
Hannah's age. Mark is older than Tom. How old is Tom?
(a) 31 (b) 32 (c) 33 (d) 34 (e) None of the above
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Hannah, Mark and Tom have a combined age of 68.
h + m + t = 68
:
Hannah is twice as old as the di fference between Mark and Tom's age.
h = 2(m - t)
:
Mark and Tom's combined age is 16 times Hannah's age.
m + t = 16h
-16h + m + t = 0
:
Subtract the above equation from the 1st equation
h + m + t = 68
-16h + m + t = 0
-------------------subtraction eliminates m & t, find h
17h = 68
h = 68%2F17
h = 4 yrs is Hannah's age
:
Replace h with 4 in the equation m + t = 16h
m + t = 16(4)
m + t = 64
:
Replace h in the equation h = 2(m-t)
2(m - t) = 4
Simplify, divide by 2
m - t = 2
;
Add the two equation
m + t = 64
m - t = 2
-------------
2m = 66
m = 33 yrs is Marks age
then
31 is Tom's age
:
:
Check total
4 + 33 + 31 = 68